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Concentration Phenomenon of Riemann Solutions for the Relativistic Euler Equations with the Extended Chaplygin Gas

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Abstract

The solutions of the Riemann problem for the isentropic relativistic Euler equations with the extended Chaplygin gas are constructed completely for all the possible cases. The asymptotic limits of solutions to the Riemann problem for the relativistic Euler equations are captured in detail when the equation of state of extended Chaplygin gas becomes the one of Chaplygin gas. It is shown that the formations of delta shock wave solution and two-contact-discontinuity solution are derived and analyzed rigorously during the limiting process.

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Acknowledgements

The authors would like to thank the two anonymous referees for their very valuable comments and suggestions, which improves the original manuscript greatly. This work is partially supported by Natural Science Foundation of Shandong Province (ZR2019MA019).

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  1. School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong Province, 264025, P.R. China

    Yunfeng Zhang & Meina Sun

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  1. Yunfeng Zhang
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  2. Meina Sun
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Correspondence to Meina Sun.

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This work is partially supported by Shandong Provincial Natural Science Foundation (ZR2019MA019).

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Zhang, Y., Sun, M. Concentration Phenomenon of Riemann Solutions for the Relativistic Euler Equations with the Extended Chaplygin Gas. Acta Appl Math 170, 539–568 (2020). https://doi.org/10.1007/s10440-020-00345-7

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  • DOI: https://doi.org/10.1007/s10440-020-00345-7

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