Vanishing viscosity limit of compressible non-resistive magnetohydrodynamic equations with the no-slip boundary condition

Abstract

In this paper, we consider the vanishing viscosity limit of the three dimensional compressible non-resistive magnetohydrodynamic equations with the no-slip boundary condition in the half-space. Assuming that the initial normal magnetic field is non-degenerate, by identifying a new cancellation structure in the momentum equation, we can use the tangential derivatives of solutions to control the normal derivatives of the magnetic field and pressure. Furthermore, we establish uniform regularity estimates of solutions to the initial-boundary value problem of the compressible non-resistive magnetohydrodynamic equations in conormal Sobolev spaces. Then, based on these uniform regularity estimates and the compactness arguments, the vanishing viscosity limit of solutions to the compressible non-resistive magnetohydrodynamic equations is rigorously verified in $L^{\infty }$ sense.