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Riemann problem for the isentropic relativistic Chaplygin Euler equations

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Abstract

This paper studies the Riemann problem of the isentropic relativistic Euler equations for a Chaplygin gas. The solutions exactly include five kinds. The first four consist of different contact discontinuities while the rest involves delta-shock waves. Under suitable generalized Rankine–Hugoniot relation and entropy condition, the existence and uniqueness of delta-shock solutions are established.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, People’s Republic of China

    Hongjun Cheng & Hanchun Yang

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  1. Hongjun Cheng
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  2. Hanchun Yang
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Correspondence to Hongjun Cheng.

Additional information

Supported by NNSF of China (Grant No.10961025) and Science Foundation of the Education Department of Yunnan Province (Grant No.2010Y440). This work is also supported by IRTSTYN and Scientific Research Foundation of Yunnan University (Grant No. 2011YB30).

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Cheng, H., Yang, H. Riemann problem for the isentropic relativistic Chaplygin Euler equations. Z. Angew. Math. Phys. 63, 429–440 (2012). https://doi.org/10.1007/s00033-012-0199-7

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  • DOI: https://doi.org/10.1007/s00033-012-0199-7

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