THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS

Abstract

Abstract: In this paper, we establish the existence of the global weak solutions for the nonhomogeneous incompressible magnetohydrodynamic equations with Navier boundary conditions for the velocity field and the magnetic field in a bounded domain Ω ⊂ R³. Furthermore, we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weak solutions converge to the strong one of the ideal nonhomogeneous incompressible magnetohydrodynamic equations in energy space.

Key words: nonhomogeneous incompressible MHD equations, Navier boundary conditions, inviscid and non-resistive limit

Zhipeng ZHANG. THE COMBINED INVISCID AND NON-RESISTIVE LIMIT FOR THE NONHOMOGENEOUS INCOMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH NAVIER BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2018, 38(6): 1655-1677.

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