Free boundary value problem for compressible magnetohydrodynamic equations

Abstract

In this article we consider a free boundary value problem for barotropic compressible magnetohydrodynamic equations with density-dependent viscosity coefficients. Under certain assumptions imposed on the initial data, there exists a unique global strong solution which is strictly positive after a finite time. Furthermore, the free boundaries propagate along the particle path and the domain expands outwards at an algebraic rate.