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Paper Citation Record · LEDGER

Shock formation in 1D conservation laws I: Inviscid structure

As of 18 August 2026, this Paper Citation Record lists 76 of 76 outbound references and 0 inbound Pith citation observations for arXiv:2506.17148.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.17148 v1

Coverage vector

measured 76 of 76 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:18:40.237473Z

measured 76 of 76 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

76 of 76 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1f7d6b0b-d8cb-4ae3-a13c-fa8c06a8bbf9 · outbound

This paper cites The emergence of the singular boundary from the crease in $3D$ compressible Euler flow.

Shock formation in 1D conservation laws I: Inviscid structure The emergence of the singular boundary from the crease in $3D$ compressible Euler flow

Reference 1

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation d9ec9bfa-5102-4afb-a6f3-61c7489a325d · outbound

This paper cites The relativistic Euler equations: ESI notes on their geo- analytic structures and implications for shocks in1𝐷 and multi-dimensions.

Shock formation in 1D conservation laws I: Inviscid structure The relativistic Euler equations: ESI notes on their geo- analytic structures and implications for shocks in1𝐷 and multi-dimensions

Reference 2

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 3d8de198-c118-4d90-bf9d-4646fb1a452d · outbound

This paper cites Occurrence and non-appearance of shocks in fractal Burgers equations.

Shock formation in 1D conservation laws I: Inviscid structure Occurrence and non-appearance of shocks in fractal Burgers equations

Reference 3

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation dd4dcee9-f99b-42bb-8e68-283ab737351e · outbound

This paper cites Équations aux Dérivées Partielles.

Shock formation in 1D conservation laws I: Inviscid structure Équations aux Dérivées Partielles

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.757845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation a2eeeb66-ee73-4f18-830a-4c05812038a1 · outbound

This paper cites Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions.

Shock formation in 1D conservation laws I: Inviscid structure Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation c08b8422-e1a7-4c84-8c55-eada9c9e366a · outbound

This paper cites Blowup of small data solutions for a quasilinear wave equation in two space dimensions.

Shock formation in 1D conservation laws I: Inviscid structure Blowup of small data solutions for a quasilinear wave equation in two space dimensions

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.570298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 61269557-f98d-4edb-9d42-624964dca896 · outbound

This paper cites Modelling and optimisation of flows on networks.

Shock formation in 1D conservation laws I: Inviscid structure Modelling and optimisation of flows on networks

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.433603Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 1abcdca6-a7b6-4412-87fc-68cd878a0026 · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 8

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unresolved
raw_fallback, observed 2026-08-15T19:18:43.423129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 00f6f5da-e154-4e0c-8a32-32b40748ef98 · outbound

This paper cites Low regularity ill-posedness and shock formation for 3D ideal compressible MHD.

Shock formation in 1D conservation laws I: Inviscid structure Low regularity ill-posedness and shock formation for 3D ideal compressible MHD

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.412570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation d33600b9-641f-455b-bfd0-181b97c09345 · outbound

This paper cites Low regularity ill-posedness for elastic waves driven by shock formation.

Shock formation in 1D conservation laws I: Inviscid structure Low regularity ill-posedness for elastic waves driven by shock formation

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.401168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation d62a1ae7-f107-48a2-9484-8e5328b7193f · outbound

This paper cites Low regularity ill-posedness for non-strictly hyperbolic systems in three dimensions.

Shock formation in 1D conservation laws I: Inviscid structure Low regularity ill-posedness for non-strictly hyperbolic systems in three dimensions

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.390849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 5d759ba4-efd4-4470-9c41-1d9e041da37e · outbound

This paper cites Shock formation in 1D conservation laws II: Vanishing viscosity.

Shock formation in 1D conservation laws I: Inviscid structure Shock formation in 1D conservation laws II: Vanishing viscosity

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.378994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 2b752d00-5be3-4892-ac39-fae5a0498231 · outbound

This paper cites On the front-tracking algorithm.

Shock formation in 1D conservation laws I: Inviscid structure On the front-tracking algorithm

Reference 13

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 3aeb569f-0d4f-4c29-8207-7981a23b3aae · outbound

This paper cites Global solutions of systems of conservation laws by wave-front tracking.

Shock formation in 1D conservation laws I: Inviscid structure Global solutions of systems of conservation laws by wave-front tracking

Reference 14

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation fd5e7d95-3e5e-4613-9e34-bfb71014c496 · outbound

This paper cites Hyperbolic systems of conservation laws.

Shock formation in 1D conservation laws I: Inviscid structure Hyperbolic systems of conservation laws

Reference 15

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 8e0c9043-40fe-499f-bee9-f556243d3d95 · outbound

This paper cites The unique limit of the Glimm scheme.

Shock formation in 1D conservation laws I: Inviscid structure The unique limit of the Glimm scheme

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.051180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 437813f2-5586-45ce-a805-51b6382307b4 · outbound

This paper cites Uniqueness of weak solutions to systems of conservation laws.

Shock formation in 1D conservation laws I: Inviscid structure Uniqueness of weak solutions to systems of conservation laws

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.041081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 3bbe18d1-22d3-4437-8358-bc6b6b32c662 · outbound

This paper cites Smooth self-similar implod- ing profiles to 3D compressible Euler.

Shock formation in 1D conservation laws I: Inviscid structure Smooth self-similar implod- ing profiles to 3D compressible Euler

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.031322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation a8bd2161-8100-40f4-ab9e-5bc66b1e2df8 · outbound

This paper cites Drivas, Steve Shkoller, Vlad Vicol.

Shock formation in 1D conservation laws I: Inviscid structure Drivas, Steve Shkoller, Vlad Vicol

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.020150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation b0ccc724-59e8-4995-ae81-91f1c565010d · outbound

This paper cites Formation of unstable shocks for 2D isentropic compressible Euler.

Shock formation in 1D conservation laws I: Inviscid structure Formation of unstable shocks for 2D isentropic compressible Euler

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:43.010077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation 28bd9aec-c00d-4c66-a768-c66f89a501cd · outbound

This paper cites Formation of point shocks for 3D compressible Euler.

Shock formation in 1D conservation laws I: Inviscid structure Formation of point shocks for 3D compressible Euler

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.998563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.046458Z digest=sha256:95f31076d52b7eb3024b15d1bcc0e1553696ffdf10e6449311a1eaa6cd688f9d

Observation e2f9738a-0c70-4675-9474-170b81eb6657 · outbound

This paper cites Formation of shocks for 2D isentropic com- pressible Euler.

Shock formation in 1D conservation laws I: Inviscid structure Formation of shocks for 2D isentropic com- pressible Euler

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.784502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.051050Z digest=sha256:998e581a6ac92fb5e0c17a38675ffe1ebdc365a986eb426ead20685b5e1a0966

Observation e1edd021-6ba8-47ce-b799-c0c9a1e1f0fb · outbound

This paper cites Shock formation and vorticity creation for 3D Euler.

Shock formation in 1D conservation laws I: Inviscid structure Shock formation and vorticity creation for 3D Euler

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.773663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Observation f85b7569-b755-4865-9908-c91ca6fdb587 · outbound

This paper cites Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$.

Shock formation in 1D conservation laws I: Inviscid structure Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$

Reference 24

Resolution
unresolved
no resolver link, observed 2026-08-15T19:18:39.185271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:18:39.185271Z digest=sha256:047a8e5bd3e876e5e6637dfbeadac2a184f8392f171ecee3e997be74c8ed88cd

Observation f80f330b-afea-4d44-a98a-177c6032a2b8 · outbound

This paper cites The inviscid limit of viscous Burgers at nondegenerate shock formation.

Shock formation in 1D conservation laws I: Inviscid structure The inviscid limit of viscous Burgers at nondegenerate shock formation

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.763082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.267674Z digest=sha256:08c990ad5ed87a0683b519d6bcad04cffe9ad1a082d47772fde1bba2fac55a85

Observation ce2f89bf-1405-4128-9cf0-58e138dd302d · outbound

This paper cites Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$.

Shock formation in 1D conservation laws I: Inviscid structure Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-15T19:18:39.272978Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:18:39.272978Z digest=sha256:f9db6c025d137737c8e5b5ac309375eacf3a99e14ad77c509e79a9234e85e47b

Observation 679939bd-171f-44e6-881b-4eedc2f6d60e · outbound

This paper cites Vorticity blowup in 2D compressible Euler equations.

Shock formation in 1D conservation laws I: Inviscid structure Vorticity blowup in 2D compressible Euler equations

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-15T19:18:39.276438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:18:39.276438Z digest=sha256:2ef6c0b2a69c381c18f2e56bddd4235dbdb269fd90bb93ad6c5bb32b8227d213

Observation 2197edcb-3d56-4ade-9c57-ce82375c33b4 · outbound

This paper cites Chickering, Ryan C.

Shock formation in 1D conservation laws I: Inviscid structure Chickering, Ryan C

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.751755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.280668Z digest=sha256:dbc1d6d062b86660d4545bb500b0a96cc906132fa6b714a649b10d6bc9bd930c

Observation 88b6b65e-4620-4714-a1d1-10919655d350 · outbound

This paper cites The formation of shocks in 3-dimensional fluids.

Shock formation in 1D conservation laws I: Inviscid structure The formation of shocks in 3-dimensional fluids

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.740180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.284065Z digest=sha256:867f5718d697811041098662914ed48f5bbb5a2b0fb9837bcfadaf5b18203aab

Observation f250a499-9277-45ec-ab31-eafebe6c053d · outbound

This paper cites The shock development problem.

Shock formation in 1D conservation laws I: Inviscid structure The shock development problem

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.611113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.287513Z digest=sha256:fe044e1d031244e806c5c46b368ba92a7276ad476b1bd4889ee8469533e74270

Observation 46c7ef2e-ce5c-43cc-86fc-181edab558d9 · outbound

This paper cites Shock development in spherical symmetry.

Shock formation in 1D conservation laws I: Inviscid structure Shock development in spherical symmetry

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.454731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.291508Z digest=sha256:194b413a9758efe31e541c04416ee54e892d8307401fc6ec0bcc99836b5f61f2

Observation fb5a5ca5-cc62-46cf-8839-bf814ec9e6ea · outbound

This paper cites Compressible flow and Euler’s equations.

Shock formation in 1D conservation laws I: Inviscid structure Compressible flow and Euler’s equations

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.443707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.416214Z digest=sha256:40bfaa870096e070f91f46aea9a95f19aedeec27ce040ffc13d833a0166af669

Observation bfc278ee-ed12-4814-b167-e25d1ac019a7 · outbound

This paper cites On the formation of shocks of electromagnetic plane waves in non-linear crystals.

Shock formation in 1D conservation laws I: Inviscid structure On the formation of shocks of electromagnetic plane waves in non-linear crystals

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.433610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.472436Z digest=sha256:ecb2f174a5b4e422a82d759a4c8b6f1d839b040b1dbdc47ce1bae736795dc4cd

Observation 9e5f0686-8d06-4696-adb2-cdb56d0b91a8 · outbound

This paper cites Courant, K.

Shock formation in 1D conservation laws I: Inviscid structure Courant, K

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.423290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.475777Z digest=sha256:278c92d361d16de5a9d3fb19deef5ef26a21a77842b9ad71d15ed38e817dbde7

Observation 5d5dc309-d1d8-46cf-be05-8dc9941b0206 · outbound

This paper cites Courant, D.

Shock formation in 1D conservation laws I: Inviscid structure Courant, D

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.412411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.479115Z digest=sha256:551fe6988eda66d8171bfc7df30ced6ecbdc1d08f8f472e2b5ac4c583261dc95

Observation 36145d73-61cb-4cc5-9bb2-7b32b59ce7ed · outbound

This paper cites Dafermos.

Shock formation in 1D conservation laws I: Inviscid structure Dafermos

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.401054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.482324Z digest=sha256:bd39937626a5f40df646275fa52854d778b88f88f47afc1f4e149e8f3cb66821

Observation d6c38199-c813-4cbb-9fd9-04e949540b3b · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:18:42.265469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.485713Z digest=sha256:24d01f34b27ee662e70c856e684d75abdd2310e883482ef10a524d3bcec495c7

Observation 312285c4-0717-4b48-8a46-37b3af3aa3a7 · outbound

This paper cites Finite time singularities and global well-posedness for fractal Burgers equations.

Shock formation in 1D conservation laws I: Inviscid structure Finite time singularities and global well-posedness for fractal Burgers equations

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.156343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.488831Z digest=sha256:96e84c111c28dc39c9a52c6d8a4d598411a7e34f8b53dc55ef9927fe85a45ae2

Observation 3e585e65-4d9f-404e-a713-ccefd9cc3aed · outbound

This paper cites Eperon, Harvey S.

Shock formation in 1D conservation laws I: Inviscid structure Eperon, Harvey S

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.145275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.492498Z digest=sha256:dc8df5327fdf7ff8787abfe3b67f26b0b644a43291b73dbb1f415029ee59f967

Observation 76dd5ef7-e525-4296-aa65-f012aec23b35 · outbound

This paper cites The stability of irrotational shocks and the Landau law of decay.

Shock formation in 1D conservation laws I: Inviscid structure The stability of irrotational shocks and the Landau law of decay

Reference 40

Resolution
unresolved
no resolver link, observed 2026-08-15T19:18:39.495752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:18:39.495752Z digest=sha256:e42fc8ccf63629f1fa4bfbbb6c2067564f8fb22d9225345b9ed6d280cd8fc71b

Observation 500af272-460a-49be-897e-4d4968be2a2e · outbound

This paper cites Solutions in the large for nonlinear hyperbolic systems of equations.

Shock formation in 1D conservation laws I: Inviscid structure Solutions in the large for nonlinear hyperbolic systems of equations

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.133870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.499856Z digest=sha256:ce67754b18275cb9d87237569cc2bc06281a01270d41cf15e73a161631c63c31

Observation 20d0828a-afab-4be5-a3f4-b4e75a958d50 · outbound

This paper cites Asymptotically Stable Ill-Posedness of Geometric Quasilinear Wave Equa- tions.

Shock formation in 1D conservation laws I: Inviscid structure Asymptotically Stable Ill-Posedness of Geometric Quasilinear Wave Equa- tions

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.089783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.567268Z digest=sha256:34fe7dc991415552cfa74a611fdd55f8350ee024a11f6dddd802386d52d8f101

Observation 271a6471-4c9f-4f05-9ef3-c9d512d87485 · outbound

This paper cites Formation and construction of a multidimensional shock wave for the first-order hyperbolic conservation law with smooth initial data.

Shock formation in 1D conservation laws I: Inviscid structure Formation and construction of a multidimensional shock wave for the first-order hyperbolic conservation law with smooth initial data

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:42.000223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.613019Z digest=sha256:bfd2c9d99894027c04285252cc57e6373c4a32bf247818c93adf4073e0b5a043

Observation 28803537-4b18-4be6-b487-ec366b152c66 · outbound

This paper cites Blow-up for quasilinear wave equations in three space dimensions.

Shock formation in 1D conservation laws I: Inviscid structure Blow-up for quasilinear wave equations in three space dimensions

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.989410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.616858Z digest=sha256:d096fab35e427107d052ec5862fd62aaf2d254f5550d99895c7ef502462ec47e

Observation 377564c9-22d5-4b7e-a329-ec5a0630d0e4 · outbound

This paper cites Formation of singularities in one-dimensional nonlinear wave propagation.Comm.

Shock formation in 1D conservation laws I: Inviscid structure Formation of singularities in one-dimensional nonlinear wave propagation.Comm

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.978768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.620219Z digest=sha256:39505464d3afe15ea8a1ae555b844a7653d608a8cd6edc4e369bb4a35de5c470

Observation 85f35cd3-5a07-42fd-acae-d9d987c0ee1e · outbound

This paper cites Nonlinear wave equations, formation of singularities.

Shock formation in 1D conservation laws I: Inviscid structure Nonlinear wave equations, formation of singularities

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.848639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.624129Z digest=sha256:4dcc362c9f4ef84f0f85dd95fd86e606e7dc5c6e9294658383c4ac48fcfb24d0

Observation 2a7682a2-4f69-4603-adc0-7ee9b8a916f5 · outbound

This paper cites Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications.

Shock formation in 1D conservation laws I: Inviscid structure Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.756830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.628030Z digest=sha256:2978cd62d7ebfcbd023779f0c08d403b8d61ecca6734bea3ebc83f2b30238f28

Observation c76aaca0-0bfc-4667-aa1d-db1318c2cc0b · outbound

This paper cites Keller, Lu Ting.

Shock formation in 1D conservation laws I: Inviscid structure Keller, Lu Ting

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.746937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.631823Z digest=sha256:057d6e1e0ac7d5663e953ea799f116e0a349ce51b249bb260fe6508d47549ee9

Observation 54dfe9bb-9392-4b4b-9342-9e8cffe8ff18 · outbound

This paper cites Blow up and regularity for fractal Burgers equation.

Shock formation in 1D conservation laws I: Inviscid structure Blow up and regularity for fractal Burgers equation

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.736652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.636541Z digest=sha256:8a6d09cf19851452a5da9e8a7845626abd8d1078c6f14b331d412565f923dfc8

Observation 5279e835-babe-41af-81c1-75ccc57c67d4 · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:18:41.726298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.696468Z digest=sha256:6b145549dfe6cb79d82888c806c6853353d1e3a9ebb7e4a9bd924819eac73474

Observation f4a8f885-a304-493c-b010-4b09124db73c · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:18:41.622242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.732469Z digest=sha256:fa3281e1bdf32dd375aa683d3772d45e47a7e41c503d00c77a84cbc2a399930c

Observation 89383b70-9602-4b3f-b4a0-4aafe296930d · outbound

This paper cites Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations.

Shock formation in 1D conservation laws I: Inviscid structure Development of singularities in the nonlinear waves for quasilinear hyperbolic partial differential equations

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.555672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.736376Z digest=sha256:c70f88f7f68cca596ced3e815b6706cf34a0a284b94c79b71bec21d6540dd449

Observation 60810e25-8f37-4a62-aa6a-8385be0e1168 · outbound

This paper cites Shock waves.

Shock formation in 1D conservation laws I: Inviscid structure Shock waves

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.544326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.740110Z digest=sha256:5c24e01fc3c8dd7655a7682cd830233cb3e86319feb021b0406c0cdc1457dd9f

Observation 4db608a8-6116-4ace-b409-3b14be788106 · outbound

This paper cites Shock formation in solutions to the 2D compressible Euler equa- tions in the presence of non-zero vorticity.

Shock formation in 1D conservation laws I: Inviscid structure Shock formation in solutions to the 2D compressible Euler equa- tions in the presence of non-zero vorticity

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.531707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.743998Z digest=sha256:bf5ef3660c2d74219491d4171b02fea5fc0a78c68c3c7d3bd58a8e0b15f0fdb5

Observation 71bc19b3-5f5f-45af-8862-95e8308bc3bc · outbound

This paper cites The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy.

Shock formation in 1D conservation laws I: Inviscid structure The stability of simple plane-symmetric shock formation for three-dimensional compressible Euler flow with vorticity and entropy

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.321641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.748512Z digest=sha256:c69656f9ce56a57e9d0d483b2adb450c1e05b905c44511299f76b72b8e385c9d

Observation f79e8edd-60ff-4d0b-9806-2f8dbbdd8f7d · outbound

This paper cites Mellet, A.

Shock formation in 1D conservation laws I: Inviscid structure Mellet, A

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.224857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.752919Z digest=sha256:cca184130bddf9055a36cb68349291c101c271ebe7a4b6abe21b41cd00874956

Observation 7cc013cd-50a6-4d4e-97df-7b5dd7691af4 · outbound

This paper cites On blow up for the energy super critical defocusing nonlinear Schrödinger equations.

Shock formation in 1D conservation laws I: Inviscid structure On blow up for the energy super critical defocusing nonlinear Schrödinger equations

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.212516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.756582Z digest=sha256:d52cbe0b189d8312d585721577e94800c17b9ade385bbd504f7a4d5b05ad47b2

Observation 06ac6e05-fd98-46a8-a488-9be4b883ca62 · outbound

This paper cites On the implosion of a com- pressible fluid I: Smooth self-similar inviscid profiles.

Shock formation in 1D conservation laws I: Inviscid structure On the implosion of a com- pressible fluid I: Smooth self-similar inviscid profiles

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.201669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.760979Z digest=sha256:af8bbee2d11780b41257c8faf85b236df6c5af89633b72a97d01d2303fe7500e

Observation 8a81eb3c-3c9c-426e-a5f4-a2c749bffa03 · outbound

This paper cites On the implosion of a com- pressible fluid II: Singularity formation.

Shock formation in 1D conservation laws I: Inviscid structure On the implosion of a com- pressible fluid II: Singularity formation

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.191690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.765216Z digest=sha256:685cbe08ea3e2a6470f152ce3807a438650b41694c94a65fe6be74d1addc3f64

Observation 21f3ffe1-e86f-4cfd-a88f-da6d5f863db9 · outbound

This paper cites On the formation of shocks for quasilinear wave equations.

Shock formation in 1D conservation laws I: Inviscid structure On the formation of shocks for quasilinear wave equations

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.181245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.800064Z digest=sha256:f28a6bf10b92807381d15e095929a36a00483f56c8eeedac7ee118cb266a244a

Observation f16bca8d-ec3c-4f59-abac-3fb8fb1772d8 · outbound

This paper cites A new type of stable shock formation in gas dynamics.

Shock formation in 1D conservation laws I: Inviscid structure A new type of stable shock formation in gas dynamics

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.030866Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:39.911164Z digest=sha256:9aae20b59c508540c5510e2caf25a2e5a1242dcfcd7be29e0c2826db6ca9ee6f

Observation ef017a6c-ce2d-4df1-8ee7-89ca306f5f1c · outbound

This paper cites A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy.

Shock formation in 1D conservation laws I: Inviscid structure A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:41.020897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.019378Z digest=sha256:2aaf1e4d599a38961f68bdc926b1fb86ae7440aef6bbd094bb69291c025c8abc

Observation f9c8c9d8-ae6b-4eea-8d7c-37b09e5a4b1b · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 63

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:18:41.010912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.023184Z digest=sha256:a037fd91ec39cc7367317228f2de97bababc85d40ddc0392373ccc285054eb8d

Observation 463f3e22-976f-49d3-9959-68cd7fe6c04e · outbound

This paper cites Gradient blow-up for dispersive and dissipative perturba- tions of the Burgers equation.

Shock formation in 1D conservation laws I: Inviscid structure Gradient blow-up for dispersive and dissipative perturba- tions of the Burgers equation

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.999499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.027067Z digest=sha256:0e70d9104eabff41db3f12e275b6518668c36a93f11bb7ee1d4e6e48727e89cf

Observation dc5c3f67-ae66-4572-bd44-1623a72dd44a · outbound

This paper cites BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one.

Shock formation in 1D conservation laws I: Inviscid structure BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.877763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.031722Z digest=sha256:5d994e0615e14241f9a0e76545bc9e1b6aa541c5427f5c51477acd58bf7732b2

Observation c0fcf4b2-255b-428f-ac5c-d076c9a8cf13 · outbound

This paper cites Hyperbolic partial differential equations and geometric optics.

Shock formation in 1D conservation laws I: Inviscid structure Hyperbolic partial differential equations and geometric optics

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.824302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.036513Z digest=sha256:ce8a4a35b9d500d47bccc8b9089dc2bfc0871f55ded092e34fbc00db62480c1b

Observation f6082cc1-8e23-4e65-a922-df58aef525cc · outbound

This paper cites Gesammelte mathematische Werke, wissenschaftlicher Nachlass und Nach- träge.

Shock formation in 1D conservation laws I: Inviscid structure Gesammelte mathematische Werke, wissenschaftlicher Nachlass und Nach- träge

Reference 67

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.813738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.040759Z digest=sha256:e429499da19b437684b5e29f6241035049ebe5058f56e1adf8f2f024c32a7844

Observation 374e9ae4-c660-4f57-8562-ccc7db9ffb92 · outbound

This paper cites The Cauchy problem in general relativity.

Shock formation in 1D conservation laws I: Inviscid structure The Cauchy problem in general relativity

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.803033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.044114Z digest=sha256:22c83f71c62dee75fb2918ecd5e2aa3df40c72c49ddcb3b1669fd59037281718

Observation ca75fa1b-993e-41f0-94c6-a5d52d1943e6 · outbound

This paper cites A front-tracking alternative to the random choice method.

Shock formation in 1D conservation laws I: Inviscid structure A front-tracking alternative to the random choice method

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.791347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.047593Z digest=sha256:80f16a4788f0203278216f984644fcebbdd4e6e849bb0659587b3a11c7f20ca6

Observation fe50a3a4-d458-4aef-9a73-ae5f277169ad · outbound

This paper cites The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions.

Shock formation in 1D conservation laws I: Inviscid structure The geometry of maximal development and shock formation for the Euler equations in multiple space dimensions

Reference 70

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.779964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.050655Z digest=sha256:6596abfd6f26af547b45cfd258e8df145ebb380285545b004dbff7ae46910a83

Observation a184b55a-1356-4e05-b061-f713ba14cc5e · outbound

This paper cites an unresolved cited work.

Shock formation in 1D conservation laws I: Inviscid structure Unresolved cited work

Reference 71

Resolution
unresolved
raw_fallback, observed 2026-08-15T19:18:40.767627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.053969Z digest=sha256:a98e55d63656f23639046b8d79bbc6ae15a91a76aa57df042f6e2e21a533f0a6

Observation 7c81ec44-2f46-49be-bd95-945ff5bf94ba · outbound

This paper cites Shock formation in small-data solutions to 3D quasilinear wave equations.

Shock formation in 1D conservation laws I: Inviscid structure Shock formation in small-data solutions to 3D quasilinear wave equations

Reference 72

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.690649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.132663Z digest=sha256:9ac23f1bad97080d5ec860d7208206b6a8d6e5c169518f4ca3d0e991257ca185

Observation 068a71c3-5308-474f-b671-1f36dcfd81d1 · outbound

This paper cites Stable shock formation for nearly simple outgoing plane symmetric waves.

Shock formation in 1D conservation laws I: Inviscid structure Stable shock formation for nearly simple outgoing plane symmetric waves

Reference 73

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.598568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.226254Z digest=sha256:acfb7a8a4c5805a16fc1fa483ababafa1053a442111ec6283b87d65d0108c1c4

Observation 62ec2530-8b1c-418f-9f3d-a155ea1d3efb · outbound

This paper cites Shock formation of the Burgers-Hilbert equation.

Shock formation in 1D conservation laws I: Inviscid structure Shock formation of the Burgers-Hilbert equation

Reference 74

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.587213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.229723Z digest=sha256:11ae415bc71aeeb98cc964c02f74a526ac63cb3ba057e5048b9d9413a9f7d493

Observation c3d2ce6d-00ed-4384-b7e9-188128d7a57d · outbound

This paper cites Unstable shock formation of the Burgers-Hilbert equation.

Shock formation in 1D conservation laws I: Inviscid structure Unstable shock formation of the Burgers-Hilbert equation

Reference 75

Resolution
verified exact
local_arxiv, observed 2026-08-15T19:18:40.399069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.233530Z digest=sha256:edb94b1fa2cafd1427339c9a128a58d728432db2ba7255b43bc3c26c66b01106

Observation 7f07be0f-b42d-4b4c-ab3f-392fc7cace73 · outbound

This paper cites Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data.

Shock formation in 1D conservation laws I: Inviscid structure Formation and construction of a shock wave for 3-D compressible Euler equations with the spherical initial data

Reference 76

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:18:40.545449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T19:18:40.237473Z digest=sha256:d3c5945d112861cbe5502d0b23b89ad5174d61e28328411f0b66bda97681924a

Pith citing papers

No inbound Pith citation observations are available.