Global weak solutions to a 2D compressible non-resistivity MHD system with non-monotone pressure law and nonconstant viscosity

Abstract

In this paper, we consider a two-dimensional non-resistivity MHD system describing the evolution of viscous compressible and electrically conducting fluids under the action of a vertical magnetic field, with non-monotone pressure law and density-depending viscosity λ=λ(ρ). Using an approximate scheme and the compactness method which Bresch and Jabin proposed in (Bresch and Jabin, 2018 [3]), we prove the global existence of weak solutions. This improves Li and Sun's work (Li and Sun, 2019 [32]) to more general pressure law and viscosity.