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Global weak solutions to a 2D compressible non-resistivity MHD system with non-monotone pressure law and nonconstant viscosity. (English) Zbl 1466.76048

Summary: 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 \(\lambda=\lambda(\rho)\). Using an approximate scheme and the compactness method which D. Bresch and P.-E. Jabin proposed in [Ann. Math. (2) 188, No. 2, 577–684 (2018; Zbl 1405.35133)], we prove the global existence of weak solutions. This improves Y. Li and Y. Sun’s work [J. Differ. Equations 267, No. 6, 3827–3851 (2019; Zbl 1420.35250)] to more general pressure law and viscosity.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
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