Vanishing shear viscosity limit in the magnetohydrodynamic equations. (English) Zbl 1190.76172
Summary: We study an initial boundary value problem for the equations of plane magnetohydrodynamic compressible flows, and prove that as the shear viscosity goes to zero, global weak solutions converge to a solution of the original equations with zero shear viscosity. As a by-product, this paper improves the related results obtained by Frid and Shelukhin for the case when the magnetic effect is neglected.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
initial boundary value problem; equations of plane magnetohydrodynamic compressible flows; shear viscosityReferences:
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