Global Strong and Weak Solutions to the Initial-Boundary-Value Problem of two-dimensional Compressible MHD System with Large Initial Data and Vacuum
Yazhou Chen, Bin Huang, Xiaoding Shi
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.