Ill-posedness of free boundary problem of the incompressible ideal MHD

Abstract

In the present paper, we show the ill-posedness of the free boundary problem of the incompressible ideal magnetohydrodynamics (MHD) equations in two spatial dimensions for any positive vacuum permeability ${\mu }_0$, in Sobolev spaces. The analysis is uniform for any ${\mu }_0>0$.

24 pages; improved results for any positive vacuum permeability

References in corpus (1)

• On the motion of free interface in ideal incompressible MHD

Cited by in corpus (11)

• Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics
• Well-posedness for the Linearized Free Boundary Problem of Incompressible Ideal Magnetohydrodynamics Equations
• Well-Posedness for the Free-Boundary Ideal Compressible Magnetohydrodynamic Equations with Surface Tension
• Local Well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension
• Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
• A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension
• Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics
• Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics
• Splash singularity for the free boundary incompressible viscous MHD
• A priori estimates and a blow-up criterion for the incompressible ideal MHD equations with surface tension and a closed free surface
• Well-posedness for moving interfaces in anisotropic plasmas