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

  • Lizhi Ruan
  • Yuri TrakhininEmail author


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.


Inviscid two-fluid magnetohydrodynamic flows Symmetric hyperbolic system Shock waves Characteristic discontinuities Local-in-time existence 

Mathematics Subject Classification

35L40 35L65 35L67 76W05 76T99 



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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Hubei Key Laboratory of Mathematical Physics, School of Mathematics and StatisticsCentral China Normal UniversityWuhanPeople’s Republic of China
  2. 2.Sobolev Institute of MathematicsNovosibirskRussia
  3. 3.Novosibirsk State UniversityNovosibirskRussia

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