Global strong solutions to the 3D compressible non-isentropic MHD equations with zero resistivity

Abstract

In this paper, we study the 3D compressible non-isentropic MHD equations with zero resistivity in a bounded domain. We first establish a regularity criterion for the strong solutions, and then, we combine it with an abstract bootstrap argument to prove the global well-posedness of the system under some assumptions on the viscosity coefficients and the initial data. Our results do not need the positivity of initial density, and thus, it may vanish in an open subset of the domain.