  An initial boundary value problem for compressible Magnetohydrodynamics (MHD)
is considered on an exterior domain (with the first Betti number vanishes) in
$R^3$ in this paper. The global existence of smooth solutions near a given
constant state for compressible MHD with the boundary conditions of Navier-slip
for the velocity filed and perfect conduction for the magnetic field is
established. Moreover the explicit decay rate is given. In particular, the
results obtained in this paper also imply the global existence of classical
solutions for the full compressible Navier-Stokes equations with Navier-slip
boundary conditions on exterior domains in three dimensions, which is not
available in literature, to the best of knowledge of the authors'.
