On local solutions to a free boundary problem for incompressible viscous magnetohydrodynamics in the $L_p$-approach

DOI10.4064/dm777-787-3-2021OpenAlexW3208259551MaRDI QIDQ5029008

Yoshihiro Shibata, Wojciech M. Zajączkowski

Publication date: 11 February 2022

Published in: Dissertationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/dm777-787-3-2021

zbMATH Keywords

free boundary problemincompressible magnetohydrodynamicsmodified Maxwell equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Electromagnetic theory (general) (78A25) Free boundary problems for PDEs (35R35)

Cites Work

• Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval
• On an initial-boundary value problem for the Stokes systems arising in the study of a problem with a free boundary
• On local motion of a compressible barotropic viscous fluid with the boundary slip condition
• On the Faedo-Galerkin method for a free boundary problem for incompressible viscous magnetohydrodynamics
• Free-boundary regularity for a problem arising in superconductivity
• Initial value problem for the free-boundary magnetohydrodynamics with zero magnetic boundary condition
• A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows
• Free boundary problem for the equations of magnetohydrodynamic incompressible viscous fluid
• Local existence of solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid
• Almost global solutions of the free boundary problem for the equations of a magnetohydrodynamic incompressible fluid
• Local free boundary problem for incompressible magnetohydrodynamics
• Global free boundary problem for incompressible magnetohydrodynamics
• Uniform Estimate of Viscous Free-Boundary Magnetohydrodynamics with Zero Vacuum Magnetic Field
• Nonstationary Stokes system in Besov spaces
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