On global-in-time weak solutions to a 2D full compressible non-resistive MHD system

TL;DR

This paper proves the existence of global-in-time weak solutions for a 2D full compressible non-resistive MHD system with temperature effects, using advanced mathematical techniques from fluid dynamics.

Contribution

It is the first to establish global solvability for the full compressible, viscous, non-resistive MHD system in multiple dimensions with large initial data.

Findings

Existence of global weak solutions with finite energy initial data.

Application of weak convergence and variable reduction methods to MHD systems.

First result on multi-dimensional full compressible non-resistive MHD system.

Abstract

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from compressible Navier-Stokes(- Fourier) system and the new technique of variable reduction proposed by Vasseur et al. [26] and refined by Novotny et al. [22] from compressible two-fluid models, weak solutions are shown to exist globally in time with finite energy initial data. The result is the first one on global solvability to full compressible, viscous, non-resistive magnetohydrodynamic system in multi-dimensions with large initial data.