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

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.