Nonlinear Stability of MHD Contact Discontinuities with Surface Tension

Abstract

We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface tension. The magnetic field is supposed to be nowhere tangential to the interface. This leads to the characteristic free boundary problem for contact discontinuities with surface tension in three-dimensional ideal compressible magnetohydrodynamics (MHD). We prove the nonlinear structural stability of MHD contact discontinuities with surface tension in Sobolev spaces by a modified Nash--Moser iteration scheme. The main ingredient of our proof is deriving the resolution and tame estimate of the linearized problem in usual Sobolev spaces of sufficiently large regularity. In particular, for solving the linearized problem, we introduce a suitable regularization that preserves the transport-type structure for the linearized entropy and divergence of the magnetic field.

arXiv commentTo appear in: Archive for Rational Mechanics and Analysis

References in corpus (6)

• Well-posedness of the plasma-vacuum interface problem
• Local existence of MHD contact discontinuities
• Well-Posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics
• Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime
• Well-Posedness for the Free-Boundary Ideal Compressible Magnetohydrodynamic Equations with Surface Tension
• Stability of Multidimensional Thermoelastic Contact Discontinuities

Cited by in corpus (2)

• Well-posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD
• Incompressible Limit of Compressible Ideal MHD Flows inside a Perfectly Conducting Wall