Abstract
We are concerned with a model of ideal compressible isentropic two-fluid magnetohydrodynamics (MHD). Introducing an entropy-like function, we reduce the equations of two-fluid MHD to a symmetric form which looks like the classical MHD system written in the nonconservative form in terms of the pressure, the velocity, the magnetic field and the entropy. This gives a number of instant results. In particular, we conclude that all compressive extreme shock waves exist locally in time in the limit of weak magnetic field. We write down a condition sufficient for the local-in-time existence of current-vortex sheets in two-fluid flows. For the 2D case and a particular equation of state, we make the conclusion that contact discontinuities in two-fluid MHD flows exist locally in time provided that the Rayleigh–Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at the first moment.
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The research of L.Z. Ruan was supported in part by the Natural Science Foundation of China \(\#\)11771169, \(\#\)11331005, \(\#\)11301205, \(\#\)11871236, Program for Changjiang Scholars and Innovative Research Team in University \(\#\)IRT17R46, and the Special Fund for Basic Scientific Research of Central Colleges \(\#\)CCNU18CXTD04.
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Ruan, L., Trakhinin, Y. Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD. Z. Angew. Math. Phys. 70, 17 (2019). https://doi.org/10.1007/s00033-018-1063-1
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DOI: https://doi.org/10.1007/s00033-018-1063-1