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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/296361 |
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| _version_ | 1832560244300972032 |
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| author | Gan Yin Kyungwoo Song |
| author_facet | Gan Yin Kyungwoo Song |
| author_sort | Gan Yin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-551963292c31463d96aa55bfc455686f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-551963292c31463d96aa55bfc455686f2025-02-03T01:28:05ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/296361296361Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure VanishesGan Yin0Kyungwoo Song1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, ChinaDepartment of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Republic of KoreaVanishing 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.http://dx.doi.org/10.1155/2013/296361 |
| spellingShingle | Gan Yin Kyungwoo Song Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes Abstract and Applied Analysis |
| title | Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes |
| title_full | Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes |
| title_fullStr | Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes |
| title_full_unstemmed | Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes |
| title_short | Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes |
| title_sort | limits of riemann solutions to the relativistic euler systems for chaplygin gas as pressure vanishes |
| url | http://dx.doi.org/10.1155/2013/296361 |
| work_keys_str_mv | AT ganyin limitsofriemannsolutionstotherelativisticeulersystemsforchaplygingasaspressurevanishes AT kyungwoosong limitsofriemannsolutionstotherelativisticeulersystemsforchaplygingasaspressurevanishes |