Abstract and Applied Analysis

Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes

Gan Yin and Kyungwoo Song

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Abstract

Vanishing pressure limits of Riemann solutions to relativistic Euler system for Chaplygin gas are identified and analyzed in detail. Unlike the polytropic or barotropic gas case, as the parameter decreases to a critical value, the two-shock solution converges firstly to a delta shock wave solution to the same system. It is shown that, as the parameter decreases, the strength of the delta shock increases. Then as the pressure vanishes ultimately, the solution is nothing but the delta shock wave solution to the zero pressure relativistic Euler system. Meanwhile, the two-rarefaction wave solution and the solution containing one-rarefaction wave and one-shock wave tend to the vacuum solution and the contact discontinuity solution to the zero pressure relativistic Euler system, respectively.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 296361, 15 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512210

Digital Object Identifier
doi:10.1155/2013/296361

Mathematical Reviews number (MathSciNet)
MR3143557

Zentralblatt MATH identifier
1294.35082

Citation

Yin, Gan; Song, Kyungwoo. Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes. Abstr. Appl. Anal. 2013 (2013), Article ID 296361, 15 pages. doi:10.1155/2013/296361. https://projecteuclid.org/euclid.aaa/1393512210


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