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Global existence and uniqueness of strong solutions for the magnetohydrodynamic equations. (English) Zbl 1141.76074
Summary: This paper is concerned with an initial-boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.

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