Well-posedness to the compressible viscous magnetohydrodynamic system

This paper is concerned with the Cauchy problem of the compressible viscous magnetohydrodynamic (MHD) system in whole spatial space RdRd for d⩾3d⩾3. It is shown that the global solution exists uniquely in hybrid Besov spaces provided the initial data close to a constant equilibrium state away from the vacuum.