  The authors study the Cauchy problem of the magnetohydrodynamic equations for
viscous compressible barotropic flows in two or three spatial dimensions with
vacuum as far field density. For two spatial dimensions, we establish the
global existence and uniqueness of strong solutions (which may be of possibly
large oscillations) provided the smooth initial data are of small total energy,
and obtain some a priori decay with rates (in large time) for the pressure, the
spatial gradient of both the velocity field and the magnetic field. Moreover,
for three spatial dimensions case, some similar decay rates are also obtained.
