Uniform regularity and vanishing viscosity limit for the 2D heat-conducting compressible MHD system in half-space

In this paper, we are concerned with the uniform regularity of the solution for the initial boundary value problem of a 2D compressible magnetohydrodynamic (MHD) system with heat conduction, as well as the vanishing viscosity limit in a half-space. In particular, the velocity field is governed by the no-slip boundary condition, while the temperature is subject to the zero Neumann boundary condition. In a suitable functional framework based on conormal Sobolev spaces, we derive a uniform estimate for the compressible MHD system, under the assumption that the initial magnetic field is transverse to the boundary. As an application of this uniform regularity, we prove the asymptotic equivalence between the solution of the viscous MHD system and the ideal MHD system in the L ∞ sense by some compactness arguments.