Maximal entropy production principle and the Euler system of gas dynamics
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913162685579264 |
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| author | Chiodaroli, Elisabetta Feireisl, Eduard Kreml, Ondřej Markfelder, Simon |
| author_facet | Chiodaroli, Elisabetta Feireisl, Eduard Kreml, Ondřej Markfelder, Simon |
| contents | Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically relevant solution can be selected by maximizing the entropy production rate. Firstly, we present an example of Riemann initial data in 2-D, for which the standard self-similar solution fails to satisfy the maximal entropy production principle. Hence, maximizing the entropy production rate rules out the 1-D self-similar solution which intuitively seems to be the physically relevant solution in this context. Secondly, we show for a large class of initial data that there exist entropy admissible weak solutions with an arbitrary (non-decreasing) total entropy profile. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26687 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal entropy production principle and the Euler system of gas dynamics Chiodaroli, Elisabetta Feireisl, Eduard Kreml, Ondřej Markfelder, Simon Analysis of PDEs 35L65, 35Q31, 76N10 Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically relevant solution can be selected by maximizing the entropy production rate. Firstly, we present an example of Riemann initial data in 2-D, for which the standard self-similar solution fails to satisfy the maximal entropy production principle. Hence, maximizing the entropy production rate rules out the 1-D self-similar solution which intuitively seems to be the physically relevant solution in this context. Secondly, we show for a large class of initial data that there exist entropy admissible weak solutions with an arbitrary (non-decreasing) total entropy profile. |
| title | Maximal entropy production principle and the Euler system of gas dynamics |
| topic | Analysis of PDEs 35L65, 35Q31, 76N10 |
| url | https://arxiv.org/abs/2605.26687 |