TY - JOUR

T1 - Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD

AU - Ruan, Lizhi

AU - Trakhinin, Yuri

PY - 2019/2/1

Y1 - 2019/2/1

N2 - 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.

AB - 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.

KW - Characteristic discontinuities

KW - Inviscid two-fluid magnetohydrodynamic flows

KW - Local-in-time existence

KW - Shock waves

KW - Symmetric hyperbolic system

KW - CURRENT-VORTEX SHEETS

KW - EXISTENCE

KW - STABILITY

KW - SYSTEMS

KW - GLOBAL WELL-POSEDNESS

UR - http://www.scopus.com/inward/record.url?scp=85058927648&partnerID=8YFLogxK

U2 - 10.1007/s00033-018-1063-1

DO - 10.1007/s00033-018-1063-1

M3 - Article

AN - SCOPUS:85058927648

VL - 70

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 1

M1 - 17

ER -