Paper Citation Record · LEDGER

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler

As of 12 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2412.21040.

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pith.paper-citation-record.v1
2412.21040 v2

Coverage vector

measured 44 of 44 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-10T23:10:38.064428Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

44 of 44 outbound references displayed

verified exact1
verified fuzzy35
unresolved8
parse uncertain0
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External citation measurements

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Outbound references

Observation 3b09c381-2266-4b3c-9c71-2130dc755b97 · outbound

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

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

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.862884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a8b39d7-029b-4b99-bfd7-410b455e7ef2 · outbound

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

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

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.868461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2de9c21f-2899-42ba-bfd4-30f0cea31269 · outbound

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

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.741510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e366cecd-4b60-4128-98eb-dda2382bc8f6 · outbound

This paper cites Plane algebraic curves.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Plane algebraic curves

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.726500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 05b87e89-5e74-4fff-a1d4-bbcbd1bb35b6 · outbound

This paper cites Smooth imploding solutions for 3D compressible fluids.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Smooth imploding solutions for 3D compressible fluids

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.883736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffbaa80f-3920-4132-9bf3-b7b581948120 · outbound

This paper cites Simultaneous development of shocks and cusp s for 2d euler with azimuthal symmetry from smooth data.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.711540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ec2d2571-720e-4834-85d9-273c4b5a4e3a · outbound

This paper cites Formation and development of singularitiesfor the compressible Euler equations.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.695658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 01b62fd9-50a8-4d84-a0e3-95a8d0d6e0b1 · outbound

This paper cites Formation of unstab le shocks for 2D insentropic compressible Euler.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.679951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 719f69df-171f-4881-b9cb-9a3403db20e9 · outbound

This paper cites For mation of shocks for 2D isentropic compressible Euler.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.665895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f14e83d1-deaf-499f-a52e-c24f05133c6f · outbound

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

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.651936Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dc72a67f-8951-45f6-a519-61d431545cb2 · outbound

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

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.638119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6c3fdf6a-18c4-4cd8-8a87-8239bda521fc · outbound

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

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

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.917137Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9181d9c2-af74-4c04-924b-8a808865d52c · outbound

This paper cites Optimal time-dependent lower bound on densi ty for classical solutions of 1-d compressible euler equati ons.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.623877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c96a345a-de52-4f4c-bb7a-981c8859fc88 · outbound

This paper cites Shock forma tion in the compressible euler equations and related system s.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.608590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e55aace5-9655-4c4d-a2b5-61b681eb1661 · outbound

This paper cites The Cauchy problem for th e Euler equations for compressible ﬂuids.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.593556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d48b7602-e5d5-4dac-9548-02fea121b64e · outbound

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

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

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.935698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4b4811f-8a9e-4fea-9d1a-a5cfc1f820af · outbound

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

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Vorticity blowup in 2D compressible Euler equations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-10T23:10:37.940278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e17b227e-0d0c-4cc3-92df-603754dea60f · outbound

This paper cites Formation and constructi on of shock for p-system.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.578731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 61a39831-a9c8-421c-b6b7-2d83d18d8c40 · outbound

This paper cites The formation of shocks in 3-dimensional ﬂuids , volume 2.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.563616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 174ae939-0aaa-4701-8e3b-d63e666e23e7 · outbound

This paper cites The shock development problem.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler The shock development problem

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.548941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bd432c19-3b4b-48d5-ae34-583f9700232e · outbound

This paper cites Shock dev elopment in spherical symmetry.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Shock dev elopment in spherical symmetry

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.534701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 88fd5850-57c8-4cec-a08f-f71ba37f05c1 · outbound

This paper cites Compressible ﬂow and Euler’s equations , volume 9 of Surveys of Modern Mathematics.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.519835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fcad9b68-2e01-4ed9-af3a-ef5433a0045a · outbound

This paper cites Singularity formation for burgers equation with transvers e viscosity.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.505492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d1725ab8-bf10-4ea1-95ae-ed9a0aaca2ae · outbound

This paper cites Supersonic Flow and Shock Waves.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Supersonic Flow and Shock Waves

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.489615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 74f27427-ceca-403c-a910-f00cd18e5341 · outbound

This paper cites Hyperbolic conservation laws in continuum physics , volume 3.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Hyperbolic conservation laws in continuum physics , volume 3

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.474239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2e32e437-87e8-4365-bfa7-cd6fe5e08f59 · outbound

This paper cites Formation of singularities in one-dimensi onal nonlinear wave propagation.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.459010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7017ca06-24a2-4d27-9d96-26742f4f85cf · outbound

This paper cites Formation and propagation of singularit ies for 2 × 2 quasilinear hyperbolic systems.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.444436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5c71e44d-c65c-4aa1-bb98-40ecf2e8900d · outbound

This paper cites Landau and Evgeny M.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Landau and Evgeny M

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.429871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3f0bd4f6-9f66-494b-a779-db15dec93aab · outbound

This paper cites an unresolved cited work.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:10:38.415016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7f64b96a-cd62-47e0-afb0-942efdeb58c4 · outbound

This paper cites Description de la formation d’un choc dans le p-système.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.400604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 480985d8-e5c6-4558-be90-943ab4ba25d7 · outbound

This paper cites Development of singularities in the nonl inear waves for quasi-linear hyperbolic partial different ial equations.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.386575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d74c6782-90d5-4513-bffa-b10efed99dab · outbound

This paper cites Shock waves, volume 215 of Graduate Studies in Mathematics.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.370884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fb7b09a2-bd3e-4180-9317-e0bd5812399d · outbound

This paper cites Shock formation in soluti ons to the 2d compressible euler equations in the presence of non-zero vorticity.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.355196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 33b021d3-e705-4a01-87b4-5dda054773c8 · outbound

This paper cites The stability of simple pl ane-symmetric shock formation for three-dimensional comp ressible Euler ﬂow with vorticity and entropy.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.340376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 45abd67a-bac8-4ccf-8eb1-999c734e58d4 · outbound

This paper cites Compressible ﬂuid ﬂow and systems of conservation laws in se veral space variables, volume 53.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.324540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 43a69f7f-2bc1-4376-915e-973440043b61 · outbound

This paper cites On the implosion of a compressible ﬂuid I: smoot h self-similar inviscid proﬁle.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.309773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2de56a75-32ec-4ef2-b467-921d8c937538 · outbound

This paper cites On the implosion of a compressible ﬂuid II: sing ularity formation.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.294889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7aa0e490-22d4-4ff4-9ae7-4e263211abaa · outbound

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

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.280176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 365eecdc-4acf-4064-8d2d-5b298fd948dd · outbound

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

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

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:10:38.109742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7e3926da-fd9e-407d-942b-fd1dca7b60de · outbound

This paper cites Gradient blow-u p for dispersive and dissipative perturbations of the Burge rs equation.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.265005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b775369d-49cb-4769-b854-faf7a14dd86e · outbound

This paper cites Über die Fortpﬂanzung ebener Luftwe llen von endlicher Schwingungsweite.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.250183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cc34ab36-d9a5-4175-bf08-bdb490699f11 · outbound

This paper cites The geometry of maximal d evelopment and shock formation for the Euler equations in mu ltiple space dimen- sions.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.234721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 27c9605e-5c31-4a31-b4a7-f1836a4a8df3 · outbound

This paper cites an unresolved cited work.

Gradient catastrophes and an infinite hierarchy of H\"older cusp-singularities for 1D Euler Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:10:38.216932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a5de187f-7e52-431f-b83f-18dcaf9151f6 · outbound

This paper cites Formation and construction of a shock wav e for 3-D compressible Euler equations with the spherical in itial data.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:10:38.203011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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