Uniform estimate of viscous free-boundary Magnetohydrodynamics with zero vacuum magnetic field

Abstract

We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in ${\mathbb{R}}^3$, especially when vacuum magnetic field is identically zero. It is a central problem in mathematics to perform vanishing viscosity limit to get a solution of hyperbolic inviscid system. However, boundary layer behavior happens near the free-boundary, so existence time $T^{\epsilon }\to 0$ as kinematic viscosity $\epsilon \to 0$ in standard sobolev space. Inspired by \cite{NMFR1}, we use sobolev conormal space to derive uniform regularity in viscosity $\epsilon$. Finally, we get a solution of inviscid free-boundary magnetohydrodynamics when initial magnetic field is zero on the free-boundary and in vacuum.

57 pages

References in corpus (1)

• A Priori Estimates for the Free Boundary Problem of Incompressible Neo-Hookean Elastodynamics

Cited by in corpus (1)

• On the motion of free interface in two-dimensional ideal incompressible MHD