Maximal dissipation and well-posedness of the Euler system of gas dynamics
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917899192500224 |
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| author | Feireisl, Eduard Jüngel, Ansgar Lukáčová-Medvid'ová, Mária |
| author_facet | Feireisl, Eduard Jüngel, Ansgar Lukáčová-Medvid'ová, Mária |
| contents | We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two step, selection procedure to identify a unique semigroup solution in the class of dissipative solutions to the Euler system. Finally, we introduce a refined version of Dafermos' criterion yielding a unique solution of the problem for any finite energy initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05134 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal dissipation and well-posedness of the Euler system of gas dynamics Feireisl, Eduard Jüngel, Ansgar Lukáčová-Medvid'ová, Mária Analysis of PDEs 35Q31, 76N10, 35B65, 35D99, 35F50 We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two step, selection procedure to identify a unique semigroup solution in the class of dissipative solutions to the Euler system. Finally, we introduce a refined version of Dafermos' criterion yielding a unique solution of the problem for any finite energy initial data. |
| title | Maximal dissipation and well-posedness of the Euler system of gas dynamics |
| topic | Analysis of PDEs 35Q31, 76N10, 35B65, 35D99, 35F50 |
| url | https://arxiv.org/abs/2501.05134 |