On the well-posedness of a linearized plasma-vacuum interface problem in ideal compressible MHD

DOI10.1016/j.jde.2010.06.007zbMath1206.35165arXiv1005.4109OpenAlexW2964011713MaRDI QIDQ712182

Yu. L. Trakhinin

Publication date: 28 October 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4109

zbMATH Keywords

half-space problem

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Magnetohydrodynamics and electrohydrodynamics (76W05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Initial-boundary value problems for first-order hyperbolic systems (35L50) Free boundary problems for PDEs (35R35)

Related Items (30)

Local solvability of free boundary problems in ideal compressible magnetohydrodynamics with and without surface tension ⋮ Uniform Estimate of Viscous Free-Boundary Magnetohydrodynamics with Zero Vacuum Magnetic Field ⋮ Well-posedness of axially symmetric incompressible ideal magnetohydrodynamic equations with vacuum under the non-collinearity condition ⋮ Weakly nonlinear surface waves on the plasma-vacuum interface ⋮ On well-posedness of the plasma-vacuum interface problem: the case of non-elliptic interface symbol ⋮ Well-posedness of the linearized plasma-vacuum interface problem in ideal incompressible MHD ⋮ Well-posedness of the free boundary problem in incompressible MHD with surface tension ⋮ Локальное существование контактных разрывов в релятивистской магнитной гидродинамике ⋮ Well-posedness of the free boundary problem in compressible elastodynamics ⋮ On vacuum free boundary problems in ideal compressible magnetohydrodynamics ⋮ Well-posedness for moving interfaces in anisotropic plasmas ⋮ Existence and stability for the 3D linearized constant-coefficient incompressible current-vortex sheets ⋮ A higher-order Hardy-type inequality in anisotropic Sobolev spaces ⋮ Well-posedness of free boundary problem in non-relativistic and relativistic ideal compressible magnetohydrodynamics ⋮ A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows ⋮ Well-posedness of the free boundary problem for incompressible elastodynamics ⋮ On a priori energy estimates for characteristic boundary value problems ⋮ Interior penalty discontinuous Galerkin method for magnetic induction equation with resistivity ⋮ Well-Posedness of the Free Boundary Problem in Elastodynamics with Mixed Stability Condition ⋮ Local existence of MHD contact discontinuities ⋮ STABILITY OF RELATIVISTIC PLASMA-VACUUM INTERFACES ⋮ On the motion of free interface in ideal incompressible MHD ⋮ Well-posedness of the linearized problem for MHD contact discontinuities ⋮ Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition ⋮ Nonlinear surface waves on the plasma-vacuum interface ⋮ A regularity result for the incompressible magnetohydrodynamics equations with free surface boundary ⋮ Well-posedness of the plasma -- vacuum interface problem for ideal incompressible MHD ⋮ On the construction of solutions to the free-surface incompressible ideal magnetohydrodynamic equations ⋮ Lagrangian approach to global well-posedness of viscous incompressible MHD equations ⋮ On local existence of MHD contact discontinuities

Cites Work

• The fixed boundary value problems for the equations of ideal magneto- hydrodynamics with a perfectly conducting wall condition
• Well posedness for the motion of a compressible liquid with free surface boundary
• The existence of current-vortex sheets in ideal compressible magnetohydrodynamics
• The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit
• The trace theorem on anisotropic Sobolev spaces
• Some properties of anisotropic Sobolev spaces
• Existence of compressible current-vortex sheets: Variable coefficients linear analysis
• Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels
• Local existence for the free boundary problem for nonrelativistic and Relativistic compressible Euler equations with a vacuum boundary condition
• An energy principle for hydromagnetic stability problems
• Local boundary conditions for dissipative symmetric linear differential operators
• Symmetric Positive Systems with Boundary Characteristic of Constant Multiplicity
• The existence of multidimensional shock fronts
• The equations of motion of a perfect fluid with free boundary are not well posed.
• REGULARITY OF SOLUTIONS TO CHARACTERISTIC INITIAL-BOUNDARY VALUE PROBLEMS FOR SYMMETRIZABLE SYSTEMS

This page was built for publication: On the well-posedness of a linearized plasma-vacuum interface problem in ideal compressible MHD