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The Riemann problem of conservation laws in magnetogasdynamics. (English) Zbl 1267.35127
Summary: We study the Riemann problem for a simplified model of one dimensional ideal gas in magnetogasdynamics. By using the characteristic analysis method, we prove the global existence of solutions to the Riemann problem constructively under the Lax entropy condition. The image of the contact discontinuity in magnetogasdynamics is a curve in the \((\tau, p, u)\) space. Its projection on the \((p, u)\) plane is a straight line that parallels to the \(p\)-axis. The result is more complicated and difficult than that in gas dynamics.

MSC:
35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76W05 Magnetohydrodynamics and electrohydrodynamics
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