GLOBAL STRONG AND WEAK SOLUTIONS TO THE INITIAL-BOUNDARY-VALUE PROBLEM OF TWO-DIMENSIONAL

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.

Automated summary

This paper investigates the compressible magnetohydrodynamic equations with shear viscosity and bulk viscosity in a general two-dimensional bounded domain. It proves the global existence of strong and weak solutions without restrictions on initial data size for the 2D compressible MHD system, with shear viscosity as a positive constant and bulk viscosity proportional to the density raised to a power, within certain conditions.