On Global and Decay Solution of Viscous Compressible MHD Equations

We consider in an infinite horizontal layer, the equations of the viscous compressible magnetohydrodynamic flows subject to the gravitational force. On the upper and lower planes of the layer, we consider homogeneous Dirichlet conditions on the velocity while a large constant vector field is prescribed on the magnetic field. The existence of the global strong solution with small initial data and its asymptotic behavior as time goes to infinity are established.