| Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations |
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| 作者姓名： | Gan YIN Wancheng SHENG |
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| 作者单位： | Gan YIN Wancheng SHENG Department of Mathematics，Shanghai University，Shanghai 200433，China; College of Mathematics and System Sciences，Xinjiang University，Urumqi 830046，Xinjiang，China. Department of Mathematics，Shanghai University，Shanghai 200433，China. |
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| 基金项目： | 国家自然科学基金，the Shanghai Leading Academic Discipline Project |
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| 摘 要： | The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.
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| 关 键 词： | 相对论性欧拉方程 狭义相对论 δ冲击波 真空态 |
| 收稿时间： | 1/8/2004 12:00:00 AM |
Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations |
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| Gan YIN,Wancheng SHENG.Delta Shocks and Vacuum States in Vanishing Pressure Limits of Solutions to the Relativistic Euler Equations[J].Chinese Annals of Mathematics,Series B,2008,29(6):611-622. |
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| Authors: | Gan YIN and Wancheng SHENG |
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| Institution: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, China
2. Department of Mathematics, Shanghai University, Shanghai 200433, China |
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| Abstract: | The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity. |
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| Keywords: | Relativistic Euler equations in special relativity Pressureless relativistic Euler equations Delta shock waves Vacuum Vanishing pressure limits |
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