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

Lizhi Ruan, Yuri Trakhinin

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number17
Number of pages12
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume70
Issue number1
DOIs
Publication statusPublished - 1 Feb 2019

Keywords

  • Characteristic discontinuities
  • Inviscid two-fluid magnetohydrodynamic flows
  • Local-in-time existence
  • Shock waves
  • Symmetric hyperbolic system
  • CURRENT-VORTEX SHEETS
  • EXISTENCE
  • STABILITY
  • SYSTEMS
  • GLOBAL WELL-POSEDNESS

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