TY - JOUR

T1 - Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics

AU - Trakhinin, Yu L.

PY - 2020/3/17

Y1 - 2020/3/17

N2 - We study the free boundary problem for a contact discontinuity for the system of relativistic magnetohydrodynamics. A surface of contact discontinuity is a characteristic of this system with no flow across the discontinuity for which the pressure, the velocity and the magnetic field are continuous whereas the density, the entropy and the temperature may have a jump. For the two-dimensional case, we prove the local-in-time existence in Sobolev spaces of a unique solution of the free boundary problem provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity.

AB - We study the free boundary problem for a contact discontinuity for the system of relativistic magnetohydrodynamics. A surface of contact discontinuity is a characteristic of this system with no flow across the discontinuity for which the pressure, the velocity and the magnetic field are continuous whereas the density, the entropy and the temperature may have a jump. For the two-dimensional case, we prove the local-in-time existence in Sobolev spaces of a unique solution of the free boundary problem provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity.

KW - contact discontinuity

KW - free boundary problem

KW - local-in-time existence and uniqueness theorem

KW - relativistic magnetohydrodynamics

UR - http://www.scopus.com/inward/record.url?scp=85081966029&partnerID=8YFLogxK

U2 - 10.3103/S1055134420010058

DO - 10.3103/S1055134420010058

M3 - Article

AN - SCOPUS:85081966029

VL - 30

SP - 55

EP - 76

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -