Uniform regularity estimates and inviscid limit for the compressible non-resistive magnetohydrodynamics system

We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to the small viscosity coefficient. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in L∞ sense by some compact arguments. Our results show that the transverse magnetic field near the boundary can prevent the strong boundary layers from occurring.