On the stationary magneto-convective motion of compressible full MHD equations in an infinite horizontal layer

In an infinite horizontal layer, we consider the equations of the viscous, compressible, and heat conducting magnetohydrodynamic steady flows subject to the gravitational force and to a large gradient of the temperature across the layer. As boundary conditions, we assume in the vertical directions, slip-boundary for the velocity and vertical conditions for magnetic field. The existence of a stationary solution in a small neighborhood of a steady profile close to the rest state is obtained in the Sobolev spaces as limit of a sequence of fixed points of some operators constructed from a suitable linearization of the full magnetohydrodynamic system of equations.