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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 givenconstant state for compressible MHD with the boundary conditions of Navier-slipfor the velocity filed and perfect conduction for the magnetic field isestablished. Moreover the explicit decay rate is given. In particular, theresults obtained in this paper also imply the global existence of classicalsolutions for the full compressible Navier-Stokes equations with Navier-slipboundary conditions on exterior domains in three dimensions, which is notavailable in literature, to the best of knowledge of the authors'.

nonlinearity

Global Solutions to an initial boundary problem for the compressible 3-D  MHD equations with Navier-slip and perfectly conducting boundary conditions  in exterior domains