Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 296361, 15 pages.
Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes
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.
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 296361, 15 pages.
First available in Project Euclid: 27 February 2014
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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