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

TL;DR

This paper establishes uniform regularity estimates for 2D compressible non-resistive MHD equations with boundary conditions, demonstrating the magnetic field's role in preventing boundary layers during the inviscid limit.

Contribution

It provides the first uniform conormal energy estimates for compressible MHD with boundary conditions, showing the magnetic field's influence on boundary layer prevention.

Findings

Uniform regularity estimates are achieved for solutions.

The inviscid limit from viscous to ideal MHD is proved in $L^inity$.

Transverse magnetic field prevents boundary layer formation.

Abstract

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 small viscosity coefficients. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in $L^\infty$ sense. It shows that the transverse magnetic field can prevent the boundary layers from occurring in some physical regime.