Global solvability, non-resistive limit and magnetic boundary layer of the compressible heat-conductive MHD equations

Abstract: In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive limit is justified and the convergence rates are obtained, provided the heat-conductivity satisfies some growth condition. Finally, we discuss the thickness of the magnetic boundary layer, which is particularly in consistent with the Stokes-Blasius law in the classical theory of laminar boundary layer.