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arXiv · 1810.07073

Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD

Lizhi Ruan·Yuri Trakhinin
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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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Lizhi Ruan, Yuri Trakhinin. 2018-10-15. Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD. https://doi.org/10.1007/s00033-018-1063-1

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