  In this paper we are concerned with the global well-posedness for the
compressible MHD equations with large data. We show that if the shear viscosity
$\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power
function of the density, that is, $\lambda(\rho)=\rho^{\beta}$ with $\beta>3$,
then the two dimensional compressible MHD system with the periodic boundary
conditions on the torus $\mathbb{T}^2$ have a unique global classical solution
$(\rho, u,H)$. In this work we extended the results about compressible
Navier-Stokes equations in \cite{Karzhikhov} to compressible MHD equations by
applying several new techniques to overcome the coupling between velocity and
magnetic field.
