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 (Ann. of Math., 2018), we prove the global existence of weak solutions. This improves Li and Sun's work (J. Differential Equations, 2019) to more general pressure law and viscosity.

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