Global solvability, non-resistive limit and magnetic boundary layer of the compressible heat-conductive MHD equations

TL;DR

This paper proves the global existence of solutions for 1D compressible heat-conductive MHD equations without resistivity, justifies the non-resistive limit, and analyzes the magnetic boundary layer thickness.

Contribution

It establishes the global well-posedness, convergence rates for the non-resistive limit, and characterizes the magnetic boundary layer in the compressible MHD context.

Findings

Global strong solutions exist for large data.

Convergence rates for the non-resistive limit are obtained.

Magnetic boundary layer thickness aligns with classical laminar boundary layer theory.

Abstract

In general, the resistivity is inversely proportional to the electrical conductivity, and is usually taken to be zero when the conducting fluid is of extremely high conductivity (e.g., ideal conductors). In this paper, we first establish the global well-posedness of strong solution to an initial-boundary value problem of the one-dimensional compressible, viscous, heat-conductive, non-resistive MHD equations with general heat-conductivity coefficient and large data. Then, the non-resistive limit is justified and the convergence rates are obtained, provided the heat-conductivity satisfies some growth condition. Finally, we discuss the thickness of the magnetic boundary layer, which is particularly in consistent with the Stokes-Blasius law in the classical theory of laminar boundary layer.