Vanishing viscosity limit for viscous magnetohydrodynamic equations with a slip boundary condition

TL;DR

This paper investigates the behavior of 3-D viscous magnetohydrodynamic systems in bounded domains, focusing on the regularity and the vanishing viscosity limit under slip boundary conditions, with convergence results in high-order Sobolev spaces.

Contribution

It establishes the convergence of viscous MHD solutions to inviscid solutions in high-order Sobolev spaces under slip boundary conditions, extending understanding of boundary effects in MHD.

Findings

Convergence in H^{2k+1} Sobolev space for k>0.

Conditions on initial data ensure regularity and convergence.

Analysis of slip boundary conditions in bounded domains.

Abstract

We consider the evolutionary MHD systems, and study the the regularity and vanishing viscosity limit of the 3-D viscous system in a class of bounded domains with a slip boundary condition. We derive the convergence is in H^{2k+1}, for k>0, if the initial date holds some sufficient conditions.