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In this paper, we are concerned with the motion of electrically conductingfluid governed by the two-dimensional non-isentropic viscous compressible MHDsystem on the half plane, with no-slip condition for velocity field, perfectconducting condition for magnetic field and Dirichlet boundary condition fortemperature on the boundary. When the viscosity, heat conductivity and magneticdiffusivity coefficients tend to zero in the same rate, there is a boundarylayer that is described by a Prandtl-type system. By applying a coordinatetransformation in terms of stream function as motivated by the recent work\cite{liu2016mhdboundarylayer} on the incompressible MHD system, under thenon-degeneracy condition on the tangential magnetic field, we obtain thelocal-in-time well-posedness of the boundary layer system in weighted Sobolevspaces.

Local-in-time well-posedness for Compressible MHD boundary layer