On strong solutions to the Cauchy problem of the two-dimensional compressible magnetohydrodynamic equations with vacuum

Two-dimensional barotropic compressible magnetohydrodynamic equations with shear and bulk viscosities being a positive constant and a power function of the density, respectively, are considered. We prove that the Cauchy problem on the whole two-dimensional space with vacuum as the far field density admits a unique local strong solution provided the initial density and magnetic field do not decay very slowly at infinity. In particular, the initial density can have a compact support.