Global Strong and Weak Solutions to the Initial-Boundary-Value Problem of two-dimensional Compressible MHD System with Large Initial Data and Vacuum

Abstract

In this paper, we study the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional (2D) bounded simply connected domain. For initial density allowed to vanish, we prove that the initial-boundary-value problem of a 2D compressible MHD system admits the global strong and weak solutions without any restrictions on the size of initial data provided the shear viscosity is a positive constant and the bulk one is $\lambda=\rho^\beta$ with $\beta>4/3$. As we known, this is the first result concerning the global existence of strong solutions to the compressible MHD system in general two-dimensional bounded domains with large initial data and vacuum.