Chen, Gui-Qiang G;
Schrecker, Matthew R;
(2022)
Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations.
Annals of PDE
, 8
(1)
, Article 10. 10.1007/s40818-022-00123-8.
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Abstract
We analyze the relativistic Euler equations of conservation laws of baryon number and momentum with a general pressure law. The existence of global-in-time bounded entropy solutions for the system is established by developing a compensated compactness framework. The proof relies on a careful analysis of the entropy and entropy-flux functions, which are represented by the fundamental solutions of the entropy and entropy-flux equations for the relativistic Euler equations. Based on a careful entropy analysis, we establish the compactness framework for sequences of both exact solutions and approximate solutions of the relativistic Euler equations. Then we construct approximate solutions via the vanishing viscosity method and employ our compactness framework to deduce the global-in-time existence of entropy solutions. The compactness of the solution operator is also established. Finally, we apply our techniques to establish the convergence of the Newtonian limit from the entropy solutions of the relativistic Euler equations to the classical Euler equations.
| Type: | Article |
|---|---|
| Title: | Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s40818-022-00123-8 |
| Publisher version: | https://doi.org/10.1007/s40818-022-00123-8 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Relativistic Euler equations, entropy solutions, Newtonian limit, compactness, solution operator, vanishing viscosity method, entropy kernel, entropy-flux kernel, fundamental solutions, compensated compactness |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10149482 |
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