Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T23:10:38.064428Z
Paper Citation Record · LEDGER
As of 11 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2412.21040.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T23:10:38.064428Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
44 of 44 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 3b09c381-2266-4b3c-9c71-2130dc755b97 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The emergence of the singular boundary from the crease in $3D$ compressible Euler flow
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2a8b39d7-029b-4b99-bfd7-410b455e7ef2 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2de9c21f-2899-42ba-bfd4-30f0cea31269 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Blowup of small data solutions for a quasi linear wave equation in two space dimensions
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e366cecd-4b60-4128-98eb-dda2382bc8f6 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Plane algebraic curves
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 05b87e89-5e74-4fff-a1d4-bbcbd1bb35b6 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Smooth imploding solutions for 3D compressible fluids
Reference 5
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ffbaa80f-3920-4132-9bf3-b7b581948120 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Simultaneous development of shocks and cusp s for 2d euler with azimuthal symmetry from smooth data
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation ec2d2571-720e-4834-85d9-273c4b5a4e3a · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation and development of singularitiesfor the compressible Euler equations
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 01b62fd9-50a8-4d84-a0e3-95a8d0d6e0b1 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation of unstab le shocks for 2D insentropic compressible Euler
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 719f69df-171f-4881-b9cb-9a3403db20e9 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler For mation of shocks for 2D isentropic compressible Euler
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f14e83d1-deaf-499f-a52e-c24f05133c6f · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Fo rmation of point shocks for 3D compressible Euler
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation dc72a67f-8951-45f6-a519-61d431545cb2 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Sh ock formation and vorticity creation for 3D Euler
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 6c3fdf6a-18c4-4cd8-8a87-8239bda521fc · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9181d9c2-af74-4c04-924b-8a808865d52c · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Optimal time-dependent lower bound on densi ty for classical solutions of 1-d compressible euler equati ons
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c96a345a-de52-4f4c-bb7a-981c8859fc88 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Shock forma tion in the compressible euler equations and related system s
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e55aace5-9655-4c4d-a2b5-61b681eb1661 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The Cauchy problem for th e Euler equations for compressible fluids
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d48b7602-e5d5-4dac-9548-02fea121b64e · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4b4811f-8a9e-4fea-9d1a-a5cfc1f820af · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Vorticity blowup in 2D compressible Euler equations
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e17b227e-0d0c-4cc3-92df-603754dea60f · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation and constructi on of shock for p-system
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 61a39831-a9c8-421c-b6b7-2d83d18d8c40 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The formation of shocks in 3-dimensional fluids , volume 2
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 174ae939-0aaa-4701-8e3b-d63e666e23e7 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The shock development problem
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation bd432c19-3b4b-48d5-ae34-583f9700232e · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Shock dev elopment in spherical symmetry
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 88fd5850-57c8-4cec-a08f-f71ba37f05c1 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Compressible flow and Euler’s equations , volume 9 of Surveys of Modern Mathematics
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation fcad9b68-2e01-4ed9-af3a-ef5433a0045a · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Singularity formation for burgers equation with transvers e viscosity
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d1725ab8-bf10-4ea1-95ae-ed9a0aaca2ae · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Supersonic Flow and Shock Waves
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 74f27427-ceca-403c-a910-f00cd18e5341 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Hyperbolic conservation laws in continuum physics , volume 3
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2e32e437-87e8-4365-bfa7-cd6fe5e08f59 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation of singularities in one-dimensi onal nonlinear wave propagation
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7017ca06-24a2-4d27-9d96-26742f4f85cf · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation and propagation of singularit ies for 2 × 2 quasilinear hyperbolic systems
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5c71e44d-c65c-4aa1-bb98-40ecf2e8900d · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Landau and Evgeny M
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 3f0bd4f6-9f66-494b-a779-db15dec93aab · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Unresolved cited work
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7f64b96a-cd62-47e0-afb0-942efdeb58c4 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Description de la formation d’un choc dans le p-système
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 480985d8-e5c6-4558-be90-943ab4ba25d7 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Development of singularities in the nonl inear waves for quasi-linear hyperbolic partial different ial equations
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d74c6782-90d5-4513-bffa-b10efed99dab · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Shock waves, volume 215 of Graduate Studies in Mathematics
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation fb7b09a2-bd3e-4180-9317-e0bd5812399d · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Shock formation in soluti ons to the 2d compressible euler equations in the presence of non-zero vorticity
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 33b021d3-e705-4a01-87b4-5dda054773c8 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The stability of simple pl ane-symmetric shock formation for three-dimensional comp ressible Euler flow with vorticity and entropy
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 45abd67a-bac8-4ccf-8eb1-999c734e58d4 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Compressible fluid flow and systems of conservation laws in se veral space variables, volume 53
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 43a69f7f-2bc1-4376-915e-973440043b61 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler On the implosion of a compressible fluid I: smoot h self-similar inviscid profile
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2de56a75-32ec-4ef2-b467-921d8c937538 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler On the implosion of a compressible fluid II: sing ularity formation
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7aa0e490-22d4-4ff4-9ae7-4e263211abaa · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler A new type of stable shock formation in gas dynamics
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 365eecdc-4acf-4064-8d2d-5b298fd948dd · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler A characteristics approach to shock formation in 2D Euler with azimuthal symmetry and entropy
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7e3926da-fd9e-407d-942b-fd1dca7b60de · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Gradient blow-u p for dispersive and dissipative perturbations of the Burge rs equation
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation b775369d-49cb-4769-b854-faf7a14dd86e · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Über die Fortpflanzung ebener Luftwe llen von endlicher Schwingungsweite
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation cc34ab36-d9a5-4175-bf08-bdb490699f11 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The geometry of maximal d evelopment and shock formation for the Euler equations in mu ltiple space dimen- sions
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 27c9605e-5c31-4a31-b4a7-f1836a4a8df3 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Unresolved cited work
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation a5de187f-7e52-431f-b83f-18dcaf9151f6 · outbound
Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Formation and construction of a shock wav e for 3-D compressible Euler equations with the spherical in itial data
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
No inbound Pith citation observations are available.