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Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics

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Abstract

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.

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Funding

This work was supported by Mathematical Center in Akademgorodok and by the Russian Foundation for Basic Research (grant No. 19-01-00261-a).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    Yu. L. Trakhinin

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    Yu. L. Trakhinin

Authors
  1. Yu. L. Trakhinin
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Correspondence to Yu. L. Trakhinin.

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Russian Text © The Author(s), 2019, published in Matematicheskie Trudy, 2019, Vol. 22, No. 2, pp. 175–209.

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Trakhinin, Y.L. Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics. Sib. Adv. Math. 30, 55–76 (2020). https://doi.org/10.3103/S1055134420010058

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  • DOI: https://doi.org/10.3103/S1055134420010058

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