Vanishing pressure limits of Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Yin, Gan¹  Song, Kyungwoo² 

[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China

[2] Kyung Hee Univ, Dept Math, Seoul 130701, South Korea

关键词: Isentropic relativistic Euler system;    Chaplygin gas;    Riemann problem;    Vanishing pressure limit;    Delta shock wave;   

DOI  :  10.1016/j.jmaa.2013.09.050

来源: Elsevier

【 摘 要 】

The Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas with a small parameter are considered. Unlike the polytropic or barotropic gas cases, we find that firstly, as the parameter decreases to a certain critical number, the two-shock solution converges to a delta shock wave solution of the same system. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the solution is nothing but the delta shock wave solution to the zero-pressure relativistic Euler system. Meanwhile, the two-rarefaction wave solution tends to the vacuum solution to the zero-pressure relativistic system, and the solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution to the zero-pressure relativistic system as pressure vanishes. (C) 2013 Elsevier Inc. All rights reserved.

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