On some large global solutions for the compressible magnetohydrodynamic system

In this paper we consider the global well-posedness of compressible magnetohydrodynamic system in ${\mathbb{R}}^d$ with $d\ge 2$, in the framework of the critical Besov spaces. We can show that if the initial data, the shear viscosity and the magnetic diffusion coefficient are small comparing with the volume viscosity, then compressible magnetohydrodynamic system has a unique global solution.