Large bulk viscosity limit for compressible MHD equations in critical Besov spaces

TL;DR

This paper investigates the behavior of compressible MHD equations as bulk viscosity becomes very large, proving global solutions and their convergence to incompressible MHD solutions, and demonstrating magnetic reconnection in the compressible regime.

Contribution

It establishes the global well-posedness and convergence rates for compressible MHD equations in critical Besov spaces under large bulk viscosity, extending incompressible reconnection scenarios.

Findings

Proved global well-posedness of strong solutions in critical Besov spaces.

Established explicit convergence rates to incompressible MHD solutions.

Constructed smooth solutions exhibiting magnetic reconnection in the compressible regime.

Abstract

We study the large bulk viscosity limit for the compressible magnetohydrodynamics (MHD) equations in two and three dimensions. For arbitrarily large initial data in critical Besov spaces, we prove the global well-posedness of strong solutions and establish their convergence, with explicit quantitative rates, to solutions of the incompressible MHD system, as the bulk viscosity parameter tends to infinity. As an application of this singular-limit analysis, we construct global smooth solutions to the compressible MHD equations whose magnetic field undergoes reconnection, thereby extending to the compressible regime the reconnection scenarios previously identified for incompressible flows.