Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for polytropic gases |
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| Authors: | Gan Yin Wancheng Sheng |
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| Institution: | a College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, PR China
b Department of Mathematics, Shanghai University, Shanghai 200444, PR China |
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| Abstract: | The Riemann solutions for the Euler system of conservation laws of energy and momentum in special relativity for polytropic gases are considered. It is rigorously proved that, as pressure vanishes, they tend to the two kinds of Riemann solutions to the corresponding pressureless relativistic Euler equations: the one includes a delta shock, which is formed by a weighted δ-measure, and the other involves vacuum state. |
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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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