On global strong solutions to the 3D MHD flows with density-temperature-dependent viscosities

Abstract

AbstractIn this paper, we establish the global existence of strong solutions for the 3D viscous, compressible, and heat conducting magnetohydrodynamic (MHD) flows with density-temperature-dependent viscosities in a bounded domain. We essentially show that for the initial boundary value problem with initial density allowed to vanish, the strong solution exists globally under some suitable small conditions. As a byproduct, we obtain the nonlinear exponential stability of the solution.