On non-resistive limit of 1D MHD equations with no vacuum at infinity

TL;DR

This paper studies the behavior of solutions to 1D compressible MHD equations as resistivity approaches zero, establishing the non-resistive limit and global well-posedness for large initial data.

Contribution

It provides the first rigorous derivation of the non-resistive limit for 1D compressible MHD equations with large data and no vacuum at infinity.

Findings

Established resistive to non-resistive limit for strong solutions

Proved global well-posedness for resistive MHD equations

Proved global well-posedness for non-resistive MHD equations

Abstract

In this paper, we consider the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity, but the initial vacuum can be permitted inside the region. By deriving a priori $\nu $ (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for both the compressible resistive MHD equations and non-resistive MHD equations are also established, respectively.