The global solvability of the Hall-magnetohydrodynamics system in critical Sobolev spaces

DOI10.1142/S0219199721500991zbMath1502.35107arXiv1912.09194MaRDI QIDQ5048648

Jin Tan, Raphaël Danchin

Publication date: 16 November 2022

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.09194

zbMATH Keywords

Sobolev spaceswell-posednessHall-magnetohydrodynamics

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Magnetohydrodynamics and electrohydrodynamics (76W05) Meteorology and atmospheric physics (86A10) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) PDEs in connection with geophysics (35Q86) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

Related Items (5)

Well-posedness results for the 3D incompressible Hall-MHD equations ⋮ Global solutions for the incompressible Hall-magnetohydrodynamics system around constant equilibrium states ⋮ On the existence and temporal asymptotics of solutions for the two and half dimensional Hall MHD ⋮ On the global well-posedness for the compressible Hall-MHD system ⋮ Space–time decay of solutions to three-dimensional MHD equations with Hall and ion-slip effects

Cites Work

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• On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations
• On regularity criteria for the 3D Hall-MHD equations in terms of the velocity
• Fourier Analysis and Nonlinear Partial Differential Equations
• Studies on Magneto-Hydrodynamic Waves and other Anisotropic wave motions
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• Remarques sur l’Existence Globale Pour le Système de Navier–Stokes Incompressible
• On the well-posedness of the Hall-magnetohydrodynamics system in critical spaces
• Space-time decay estimates for the incompressible viscous resistive MHD and Hall-MHD equations
• On analyticity and temporal decay rates of solutions to the viscous resistive Hall-MHD system

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