Paper Citation Record · LEDGER

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous

As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2608.02330.

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2608.02330 v1

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measured 31 of 31 reference resolution

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31 of 31 outbound references displayed

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Outbound references

Observation 3e5e7c04-b981-4bf0-baae-d45701a966f3 · outbound

This paper cites On the global solution of a 3-D MHD system with initial data near equilibrium.Communications on Pure and Applied Mathematics, 70(8):1509–1561, 2017.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous On the global solution of a 3-D MHD system with initial data near equilibrium.Communications on Pure and Applied Mathematics, 70(8):1509–1561, 2017

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:29.860879Z

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Observation 96830c2e-7559-40e3-8ce7-2ee93567a10e · outbound

This paper cites Cambridge University Press, Cambridge, 1993.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Cambridge University Press, Cambridge, 1993

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:29.999221Z

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Observation 7e06b162-02dc-49bf-9ca0-abf20ab12dec · outbound

This paper cites Strong ill-posedness of the incompressible Euler equation in bor- derline Sobolev spaces.Inventiones Mathematicae, 201(1):97–157, 2015.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Strong ill-posedness of the incompressible Euler equation in bor- derline Sobolev spaces.Inventiones Mathematicae, 201(1):97–157, 2015

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.146104Z

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Observation 13f1ceca-4b15-4463-bdc2-062b97b1f9ab · outbound

This paper cites Ill-posedness of the Navier–Stokes equations in a critical space in 3D.Journal of Functional Analysis, 255(9):2233–2247, 2008.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Ill-posedness of the Navier–Stokes equations in a critical space in 3D.Journal of Functional Analysis, 255(9):2233–2247, 2008

Reference 4

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Observation 47a0aadf-4243-4d71-b8c9-8fb4dc31528e · outbound

This paper cites Global well-posedness of the incompressible magnetohydrodynamics.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Global well-posedness of the incompressible magnetohydrodynamics

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.362973Z

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Observation 745ee4a1-4b32-42f4-b97e-fac098a7bf1e · outbound

This paper cites A losing estimate for the ideal MHD equations with application to blow-up criterion.SIAM Journal on Mathematical Analysis, 38(6):1847–1859, 2007.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous A losing estimate for the ideal MHD equations with application to blow-up criterion.SIAM Journal on Mathematical Analysis, 38(6):1847–1859, 2007

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.425780Z

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Observation aae06cfe-8390-4d52-a70a-f4b3afab9d59 · outbound

This paper cites The Beale–Kato–Majda criterion for the 3D magneto-hydrodynamics equations.Communications in Mathematical Physics, 275(3):861–872, 2007.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous The Beale–Kato–Majda criterion for the 3D magneto-hydrodynamics equations.Communications in Mathematical Physics, 275(3):861–872, 2007

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.525153Z

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Observation b148d7bc-dde8-4641-bdbe-6792a004589e · outbound

This paper cites On the well-posedness of the ideal MHD equations in the Triebel–Lizorkin spaces.Archive for Rational Mechanics and Analy- sis, 195(2):561–578, 2010.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous On the well-posedness of the ideal MHD equations in the Triebel–Lizorkin spaces.Archive for Rational Mechanics and Analy- sis, 195(2):561–578, 2010

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.597103Z

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Observation 4dcfb908-7e2e-4e19-a4c6-dd7e8d9ff36a · outbound

This paper cites Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces.Journal of Functional Analysis, 286(6):110302, 2024.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces.Journal of Functional Analysis, 286(6):110302, 2024

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.717726Z

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Observation 810a0bcd-2b6f-4e4e-99a3-0e70506d59ad · outbound

This paper cites Norm Inflation for Inviscid and Fully Dissipative Boussinesq Systems in Supercritical Spaces.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Norm Inflation for Inviscid and Fully Dissipative Boussinesq Systems in Supercritical Spaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:30.886150Z

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Observation 4fd3d3b1-6e50-4bee-8401-8055f2bd1d64 · outbound

This paper cites In´ equations en thermo´ elasticit´ e et magn´ etohydrodynamique.Archive for Rational Mechanics and Analysis, 46(4):241–279, 1972.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous In´ equations en thermo´ elasticit´ e et magn´ etohydrodynamique.Archive for Rational Mechanics and Analysis, 46(4):241–279, 1972

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.037107Z

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Observation 2ed5a417-6e1f-426c-b81a-150e8aad97d5 · outbound

This paper cites Fefferman, David S.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Fefferman, David S

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.192277Z

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Observation 7cd0a20e-aec1-413c-992e-5e2771951e0d · outbound

This paper cites Fefferman, David S.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Fefferman, David S

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.342168Z

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Observation 65f207ed-b7db-4ee8-a9df-a086a539093e · outbound

This paper cites On the global well-posedness of the 3D axisymmetric resistive MHD equations.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous On the global well-posedness of the 3D axisymmetric resistive MHD equations

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.469081Z

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Observation 63e3a2f2-d45c-41ff-96bf-532a0462a4d0 · outbound

This paper cites On global dynamics of three dimensional magnetohydrody- namics: nonlinear stability of Alfv´ en waves.Annals of PDE, 4(1):5, 2018.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous On global dynamics of three dimensional magnetohydrody- namics: nonlinear stability of Alfv´ en waves.Annals of PDE, 4(1):5, 2018

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.600708Z

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Observation 0249325b-0cad-4419-99a2-0a675bcfd3d9 · outbound

This paper cites Commutator estimates and the Euler and Navier–Stokes equa- tions.Communications on Pure and Applied Mathematics, 41(7):891–907, 1988.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Commutator estimates and the Euler and Navier–Stokes equa- tions.Communications on Pure and Applied Mathematics, 41(7):891–907, 1988

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.719763Z

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Observation 3f232172-3386-491d-9497-e6d9f57fe6a4 · outbound

This paper cites Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces.Advances in Mathematics, 317:786–798, 2017.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces.Advances in Mathematics, 317:786–798, 2017

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:31.881577Z

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Observation bb4cb128-9346-48c6-b8f0-23a9f55dfc16 · outbound

This paper cites Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations.Advances in Mathematics, 426:109112, 2023.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations.Advances in Mathematics, 426:109112, 2023

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.057152Z

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Observation 91a877af-e0db-449d-889b-7f5d472ba507 · outbound

This paper cites Non-uniqueness of weak solutions to 3D magnetohy- drodynamic equations.Journal de Math´ ematiques Pures et Appliqu´ ees, 165:232–285, 2022.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Non-uniqueness of weak solutions to 3D magnetohy- drodynamic equations.Journal de Math´ ematiques Pures et Appliqu´ ees, 165:232–285, 2022

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.256534Z

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Observation 417fcb74-8e99-4b2a-8f4e-e7e32731417c · outbound

This paper cites Sharp non-uniqueness of weak solutions to 3D magnetohydrodynamic equations: beyond the Lions exponent.Journal of Functional Analysis, 287(7):110528, 2024.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Sharp non-uniqueness of weak solutions to 3D magnetohydrodynamic equations: beyond the Lions exponent.Journal of Functional Analysis, 287(7):110528, 2024

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.371814Z

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Observation 96b7fb3e-8c08-48ef-9b5c-24aa481e36e8 · outbound

This paper cites Illposedness of incompressible fluids in supercritical Sobolev spaces.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Illposedness of incompressible fluids in supercritical Sobolev spaces

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.575974Z

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Observation aba1119a-c59f-49de-a179-474884861a22 · outbound

This paper cites Sharp norm inflation for 3D Navier-Stokes equations in supercritical spaces.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Sharp norm inflation for 3D Navier-Stokes equations in supercritical spaces

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.721197Z

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Observation 8bc456dd-645f-4770-a3a8-2bb2a12f614a · outbound

This paper cites Applied Mathematical Sciences, volume 53.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Applied Mathematical Sciences, volume 53

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:32.860305Z

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Observation deaf241f-f4c8-412c-9b88-d5f76fe1d6b1 · outbound

This paper cites Cambridge University Press, Cambridge, 2000.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Cambridge University Press, Cambridge, 2000

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.031891Z

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Observation 97a61ab7-f684-4ff0-bfa9-49901c46dff9 · outbound

This paper cites Some mathematical questions related to the MHD equa- tions.Communications on Pure and Applied Mathematics, 36(5):635–664, 1983.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Some mathematical questions related to the MHD equa- tions.Communications on Pure and Applied Mathematics, 36(5):635–664, 1983

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.191138Z

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Observation 8bd6f254-2f06-457b-bc6c-6d498f665220 · outbound

This paper cites Global well-posedness of the MHD equations in a homogeneous magnetic field.Analysis & PDE, 10(6):1361–1406, 2017.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Global well-posedness of the MHD equations in a homogeneous magnetic field.Analysis & PDE, 10(6):1361–1406, 2017

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.289261Z

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Observation d9150968-7ce4-4d8b-8907-97fcef638734 · outbound

This paper cites Global well-posedness of the MHD equations via the comparison principle.Science China Mathematics, 61(11):2111–2120, 2018.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Global well-posedness of the MHD equations via the comparison principle.Science China Mathematics, 61(11):2111–2120, 2018

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.462859Z

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Observation 95580104-84f5-4d29-8e5c-81c55faf055d · outbound

This paper cites Global well-posedness for the 2-D MHD equations with magnetic diffusion.Communications in Mathematical Research, 36(4):377–389, 2020.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Global well-posedness for the 2-D MHD equations with magnetic diffusion.Communications in Mathematical Research, 36(4):377–389, 2020

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.617636Z

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Observation 3b6722e7-f945-49ab-ba1e-bc7398367f5f · outbound

This paper cites Generalized MHD equations.Journal of Differential Equations, 195(2):284–312, 2003.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Generalized MHD equations.Journal of Differential Equations, 195(2):284–312, 2003

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.772329Z

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Observation d5bac940-4280-42ae-a757-2d2d646bb819 · outbound

This paper cites Mild ill-posedness inL ∞ for 2D resistive MHD equations near a background magnetic field.International Mathematics Research Notices, 2023(6):4839–4868, 2023.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Mild ill-posedness inL ∞ for 2D resistive MHD equations near a background magnetic field.International Mathematics Research Notices, 2023(6):4839–4868, 2023

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.871912Z

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Observation 5c084148-6bac-49a5-8b07-582fe5be46cf · outbound

This paper cites Global small solutions to three-dimensional incompressible magnetohy- drodynamical system.SIAM Journal on Mathematical Analysis, 47(1):26–65, 2015.

Strong ill-posedness for the MHD system in the supercritical regime: inviscid and viscous Global small solutions to three-dimensional incompressible magnetohy- drodynamical system.SIAM Journal on Mathematical Analysis, 47(1):26–65, 2015

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T09:22:33.958711Z

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