Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-25T00:49:55.055953Z
Paper Citation Record · LEDGER
Formation of shocks for 2D isentropic compressible Euler
As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1907.03784.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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
Reference resolution
43 of 43 outbound references displayed
- verified exact7
- verified fuzzy30
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 22ea2792-b9f2-48f2-b551-3bd767899b8f · outbound
This paper cites Alinhac, Blowup of small data solutions for a class of quasilinear wav e equations in two space dimensions.
Formation of shocks for 2D isentropic compressible Euler Alinhac, Blowup of small data solutions for a class of quasilinear wav e equations in two space dimensions
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.782527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 47207c79-a91c-45cd-9c58-f70ef186213f · outbound
This paper cites Alinhac, Blowup of small data solutions for a quasilinear wave equati on in two space dimensions , Ann.
Formation of shocks for 2D isentropic compressible Euler Alinhac, Blowup of small data solutions for a quasilinear wave equati on in two space dimensions , Ann
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.730949Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d88dc68b-764b-4355-aa8b-5c3320fb9608 · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.866629Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ef923632-7fd3-4781-a226-fc865538f394 · outbound
This paper cites Chen and M.
Formation of shocks for 2D isentropic compressible Euler Chen and M
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.794283Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9e04616e-d8c9-4193-9ef7-e699b5dd2e21 · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.822637Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5f7bbcf2-275e-4c33-a5b6-0901b5ac7ba8 · outbound
This paper cites On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equation.
Formation of shocks for 2D isentropic compressible Euler On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equation
Reference 6
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T00:50:09.527489Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7fca8dcc-13ae-4fff-960b-aec40dd0d385 · outbound
This paper cites Christodoulou, The formation of shocks in 3-dimensional fluids, EMS Monographs in Mathematics, European Mathematical Society (EMS), Z¨ urich.
Formation of shocks for 2D isentropic compressible Euler Christodoulou, The formation of shocks in 3-dimensional fluids, EMS Monographs in Mathematics, European Mathematical Society (EMS), Z¨ urich
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.850180Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 975753f9-3104-47ed-9099-7fd6e986db99 · outbound
This paper cites Christodoulou, The shock development problem , EMS Monographs in Mathematics, European Mathematical Soc iety (EMS), Z¨ urich.
Formation of shocks for 2D isentropic compressible Euler Christodoulou, The shock development problem , EMS Monographs in Mathematics, European Mathematical Soc iety (EMS), Z¨ urich
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.764357Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7fdba965-fb83-413f-9741-820275208c1d · outbound
This paper cites Christodoulou and S.
Formation of shocks for 2D isentropic compressible Euler Christodoulou and S
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.745096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fcfd1ac9-a091-46e3-a6b5-996be52aaa85 · outbound
This paper cites Christodoulou and S.
Formation of shocks for 2D isentropic compressible Euler Christodoulou and S
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.802438Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fa748e06-100a-48de-8584-dde3a3cdf168 · outbound
This paper cites On singularity formation for the two dimensional unsteady Prandtl system around the axis.
Formation of shocks for 2D isentropic compressible Euler On singularity formation for the two dimensional unsteady Prandtl system around the axis
Reference 11
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T00:50:09.502101Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f0a3a582-9674-4fb1-9817-5d3836c513ad · outbound
This paper cites Singularity formation for Burgers equation with transverse viscosity.
Formation of shocks for 2D isentropic compressible Euler Singularity formation for Burgers equation with transverse viscosity
Reference 12
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T00:50:09.492877Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4e545333-e1e5-4e37-baad-7cab2fa976a3 · outbound
This paper cites Singularities and unsteady separation for the inviscid two-dimensional Prandtl's system.
Formation of shocks for 2D isentropic compressible Euler Singularities and unsteady separation for the inviscid two-dimensional Prandtl's system
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T00:50:09.514381Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 87519675-3c33-4815-807a-99951b9284f3 · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.722632Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e1889590-8cf5-4b79-96ac-b780654f4039 · outbound
This paper cites Separation for the stationary Prandtl equation.
Formation of shocks for 2D isentropic compressible Euler Separation for the stationary Prandtl equation
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-05-25T00:50:09.520674Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 24cc3fdb-3861-4b4d-a8e6-9331ec3741a9 · outbound
This paper cites Eggers and M.
Formation of shocks for 2D isentropic compressible Euler Eggers and M
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.726690Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 62b96f99-979e-4b87-b618-b6118c3115b4 · outbound
This paper cites Finite-Time Singularity Formation for $C^{1,\alpha}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$.
Formation of shocks for 2D isentropic compressible Euler Finite-Time Singularity Formation for $C^{1,\alpha}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$
Reference 17
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T00:50:09.507765Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4b7400ac-1c55-4f49-a39a-4bc673b45981 · outbound
This paper cites Symmetries and Critical Phenomena in Fluids.
Formation of shocks for 2D isentropic compressible Euler Symmetries and Critical Phenomena in Fluids
Reference 18
- Resolution
- verified exact
- local_arxiv, observed 2026-05-25T00:50:09.534290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 14346977-9265-43ed-bcbf-a2200a578b91 · outbound
This paper cites Giga and R.
Formation of shocks for 2D isentropic compressible Euler Giga and R
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.829746Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d632aa30-3608-47ab-bdc6-c0dcb3d549ba · outbound
This paper cites Gu` es, G.
Formation of shocks for 2D isentropic compressible Euler Gu` es, G
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.740912Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 088c3900-6acf-42f2-b2dd-5b7ce80d8247 · outbound
This paper cites Holzegel, S.
Formation of shocks for 2D isentropic compressible Euler Holzegel, S
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.767971Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation eed56806-d63a-4b75-9e57-36348fe56c5a · outbound
This paper cites John, F ormation of singularities in one-dimensional nonlinear w ave propagation, Comm.
Formation of shocks for 2D isentropic compressible Euler John, F ormation of singularities in one-dimensional nonlinear w ave propagation, Comm
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.870700Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c584ea85-fc68-45eb-9329-6204468c58ed · outbound
This paper cites Klainerman and I.
Formation of shocks for 2D isentropic compressible Euler Klainerman and I
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.858138Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e217652e-90ce-47d8-b40a-5c33e778d786 · outbound
This paper cites Klainerman, Long time behaviour of solutions to nonlinear wave equation s, Proceedings of the International Congress of Mathematicians, Vol.
Formation of shocks for 2D isentropic compressible Euler Klainerman, Long time behaviour of solutions to nonlinear wave equation s, Proceedings of the International Congress of Mathematicians, Vol
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.862770Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 30fe8fe4-3c49-4efe-b3d7-9095f17950db · outbound
This paper cites Klainerman and A.
Formation of shocks for 2D isentropic compressible Euler Klainerman and A
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.846007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 42aa3d5e-748a-4ecf-9ab3-bd151718676c · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.757170Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cf56f0f3-73e9-4c12-bdbb-7169c2731f5d · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.826105Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 67fc9102-51e0-450e-be61-8461f9f47c14 · outbound
This paper cites Luk and J.
Formation of shocks for 2D isentropic compressible Euler Luk and J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.837600Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a1a4bdb5-526b-492c-b665-7e1c08d1d0c0 · outbound
This paper cites Majda, The existence of multidimensional shock fronts , Mem.
Formation of shocks for 2D isentropic compressible Euler Majda, The existence of multidimensional shock fronts , Mem
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.854111Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6a672e4b-0a70-472f-851b-ca3cb9c3ed1f · outbound
This paper cites Majda, The stability of multidimensional shock fronts , Mem.
Formation of shocks for 2D isentropic compressible Euler Majda, The stability of multidimensional shock fronts , Mem
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.818601Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5be807bb-a18e-4376-99b2-59b2c43599db · outbound
This paper cites Majda, Compressible fluid flow and systems of conservation laws in se veral space variables , Applied Mathematical Sci- ences, vol.
Formation of shocks for 2D isentropic compressible Euler Majda, Compressible fluid flow and systems of conservation laws in se veral space variables , Applied Mathematical Sci- ences, vol
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.841813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1cf92c40-f4c9-4a32-bce9-7ee9899f1d97 · outbound
This paper cites Martel, F.
Formation of shocks for 2D isentropic compressible Euler Martel, F
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.833544Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 71800237-2710-4af4-9464-669f657d8492 · outbound
This paper cites Merle, Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schr¨ odinger equation , Ann.
Formation of shocks for 2D isentropic compressible Euler Merle, Asymptotics for L2 minimal blow-up solutions of critical nonlinear Schr¨ odinger equation , Ann
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.798516Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0bc09fb2-e7b4-46cf-b389-49c8cb6ebd91 · outbound
This paper cites Merle and P.
Formation of shocks for 2D isentropic compressible Euler Merle and P
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.814705Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9c5101a9-3c11-4e7e-a87a-08ee16a2d2d2 · outbound
This paper cites Merle, P.
Formation of shocks for 2D isentropic compressible Euler Merle, P
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.790512Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation da8c8876-2520-4f6c-bb3d-a7137ab86f91 · outbound
This paper cites Merle and H.
Formation of shocks for 2D isentropic compressible Euler Merle and H
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.810848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 42587848-6c0d-47b1-9d7e-585e235b6d2e · outbound
This paper cites Merle and H.
Formation of shocks for 2D isentropic compressible Euler Merle and H
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.760768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0f0d3fd5-5f91-48c9-9333-be06a5f5da69 · outbound
This paper cites M´ etivier,Stability of multidimensional shocks , Advances in the theory of shock waves, 2001, pp.
Formation of shocks for 2D isentropic compressible Euler M´ etivier,Stability of multidimensional shocks , Advances in the theory of shock waves, 2001, pp
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.778604Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5e1ddc9f-370c-47bc-8405-dad8a7adef1c · outbound
This paper cites Miao and P.
Formation of shocks for 2D isentropic compressible Euler Miao and P
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.771558Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4c7fc5e2-b196-42e7-8b6b-95823aea3fbb · outbound
This paper cites Pomeau, M.
Formation of shocks for 2D isentropic compressible Euler Pomeau, M
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.735055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1129f80a-6707-4b26-b5ee-1b4888a30bdb · outbound
This paper cites Riemann, ¨Uber die Fortpflanzung ebener Luftwellen von endlicher Schw ingungsweite, Abhandlungen der K¨ oniglichen Gesellschaft der Wissenschaften in G¨ ottingen8 (1860), 43–66.
Formation of shocks for 2D isentropic compressible Euler Riemann, ¨Uber die Fortpflanzung ebener Luftwellen von endlicher Schw ingungsweite, Abhandlungen der K¨ oniglichen Gesellschaft der Wissenschaften in G¨ ottingen8 (1860), 43–66
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.752347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation dade649c-7b91-4373-989e-adbfddc426b3 · outbound
This paper cites an unresolved cited work.
Formation of shocks for 2D isentropic compressible Euler Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-05-25T00:50:09.786303Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9156bdfb-c9cf-4f42-b389-07d8ed6f225c · outbound
This paper cites Speck, Shock formation in small-data solutions to 3D quasilinear w ave equations, Mathematical Surveys and Monographs, vol.
Formation of shocks for 2D isentropic compressible Euler Speck, Shock formation in small-data solutions to 3D quasilinear w ave equations, Mathematical Surveys and Monographs, vol
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-25T00:50:09.806987Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
No inbound Pith citation observations are available.