  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
bounded simply connected domain. For initial density allowed to vanish, we
prove that the initial-boundary-value problem of 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
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.
