Stability of incompressible current-vortex sheets

DOI10.1016/j.jmaa.2008.06.002zbMath1175.35156OpenAlexW2043315742MaRDI QIDQ944344

Paola Trebeschi, Alessandro Morando, Yu. L. Trakhinin

Publication date: 16 September 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.06.002

zbMATH Keywords

stabilitycurrent-vortex sheetsincompressible MHD

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) A priori estimates in context of PDEs (35B45) Magnetohydrodynamics and electrohydrodynamics (76W05) Free boundary problems for PDEs (35R35) Stability and instability of magnetohydrodynamic and electrohydrodynamic flows (76E25)

Related Items (17)

Approximate current-vortex sheets near the onset of instability ⋮ Weakly nonlinear surface waves on the plasma-vacuum interface ⋮ 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 ⋮ On the weakly nonlinear Kelvin-Helmholtz instability of current-vortex sheets ⋮ A priori estimates for 3D incompressible current-vortex sheets ⋮ Existence of approximate current-vortex sheets near the onset of instability ⋮ Existence and stability for the 3D linearized constant-coefficient incompressible current-vortex sheets ⋮ Stability of the linearized MHD-Maxwell free interface problem ⋮ Well-posedness of the free boundary problem for incompressible elastodynamics ⋮ On a priori energy estimates for characteristic boundary value problems ⋮ Weakly nonlinear surface waves in magnetohydrodynamics. I ⋮ Well-Posedness of the Free Boundary Problem in Elastodynamics with Mixed Stability Condition ⋮ Well-posedness of the linearized problem for MHD contact discontinuities ⋮ Well-posedness of the two-phase flow problem in incompressible MHD ⋮ Structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics ⋮ On local existence of MHD contact discontinuities

Cites Work

• The existence of current-vortex sheets in ideal compressible magnetohydrodynamics
• The boundary value problems of mathematical physics. Transl. from the Russian by Jack Lohwater
• Some properties of anisotropic Sobolev spaces
• Existence of compressible current-vortex sheets: Variable coefficients linear analysis
• On the existence of incompressible current-vortex sheets: study of a linearized free boundary value problem
• Nonlinear compressible vortex sheets in two space dimensions
• NOTE ON A PROBLEM OF MAGNETOHYDRODYNAMIC STABILITY
• Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary
• Stability of Strong Discontinuities in Fluids and MHD
• The stability of multidimensional shock fronts
• The stability of compressible vortex sheets in two space dimensions
• Dissipative Symmetrizers of Hyperbolic Problems and Their Applications to Shock Waves and Characteristic Discontinuities
• Initial boundary value problems for hyperbolic systems

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