A note on the inviscid limit of the incompressible MHD equations

TL;DR

This paper proves that solutions of the viscous and resistive incompressible MHD equations converge to the ideal MHD solutions as viscosity and resistivity vanish, using a specific analytical method.

Contribution

It establishes the convergence of viscous and resistive MHD solutions to ideal MHD solutions in the zero-viscosity and resistivity limit, extending previous methods.

Findings

Convergence of solutions as viscosity and resistivity tend to zero

Application of a specific analytical method for proof

Supports the validity of ideal MHD as a limit case

Abstract

In this paper, we prove that as the viscosity and resistivity go to zero, the solution of the Cauchy problem for the incompressible MHD equations converges to the solution of the ideal MHD equations in the same topology with the initial data. Our proof mainly depends on the method introduced by the paper \cite{G.L.Y} and the constructions of the incompressible MHD equations.