VANISHING VISCOSITY LIMIT FOR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH TRANSVERSE BACKGROUND MAGNETIC FIELD

We are concerned with the uniform regularity estimates and vanishing viscosity limit of the solution to two-dimensional viscous compressible magnetohydrodynamic (MHD) equations with transverse background magnetic field. When the magnetic field is assumed to be transverse to the boundary and the tangential component of magnetic field satisfies zero Neumann boundary condition, even though the the no-slip velocity boundary condition is imposed, the uniform regularity estimates of the solution and its derivatives still can be achieved in suitable conormal Sobolev spaces in the half plane R-+(2), and then the vanishing viscosity limit is justified in L-infinity sense based on these uniform regularity estimates and some compactness arguments. At the same time, together with [X. Cui, S. Li, and F. Xie, Nonlinearity, 36(1):354-400, 2022], our results show that the transverse background magnetic field can prevent the strong boundary layer from occurring for compressible magnetohydrodynamics whether there is magnetic diffusion or not.