Local Smooth Solutions to the 3-Dimensional Isentropic Relativistic Euler equations |
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Authors: | Yongcai GENG and Yachun LI |
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Institution: | 1. School of Science, Shanghai Institute of Technology, Shanghai, 200235, China 2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200433, China
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Abstract: | The authors consider the local smooth solutions to the isentropic relativistic Euler equations in (3+1)-dimensional space-time for both non-vacuum and vacuum cases. The local existence is proved by symmetrizing the system and applying the Friedrichs-Lax-Kato theory of symmetric hyperbolic systems. For the non-vacuum case, according to Godunov, firstly a strictly convex entropy function is solved out, then a suitable symmetrizer to symmetrize the system is constructed. For the vacuum case, since the coefficient matrix blows-up near the vacuum, the authors use another symmetrization which is based on the generalized Riemann invariants and the normalized velocity. |
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Keywords: | Isentropic relativistic Euler equations local-in-time smooth solutions Strictly convex entropy Generalized Riemann invariants |
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