Well-posedness of the Euler system of gas dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909972358496256 |
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| author | Feireisl, Eduard Lukacova-Medvidova, Maria |
| author_facet | Feireisl, Eduard Lukacova-Medvidova, Maria |
| contents | We propose a new two-step selection criterion applicable to the dissipative measure--valued solutions of the Euler system of gas dynamics. The process consists of a successive maximisation of the entropy production rate and the total energy defect, i.e. maximisation of the turbulent energy. If the selected solution is a weak solution of the Euler system, then it is identified in the first step. Solutions selected in the second step are truly measure--valued maximising the energy defect. Accordingly, they are called turbulent solutions. The energy defect of turbulent solutions vanishes with growing time. The selected solutions depend in a Borel--measurable way on the initial data. In particular, they are almost continuously dependent on the initial data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_18267 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the Euler system of gas dynamics Feireisl, Eduard Lukacova-Medvidova, Maria Analysis of PDEs We propose a new two-step selection criterion applicable to the dissipative measure--valued solutions of the Euler system of gas dynamics. The process consists of a successive maximisation of the entropy production rate and the total energy defect, i.e. maximisation of the turbulent energy. If the selected solution is a weak solution of the Euler system, then it is identified in the first step. Solutions selected in the second step are truly measure--valued maximising the energy defect. Accordingly, they are called turbulent solutions. The energy defect of turbulent solutions vanishes with growing time. The selected solutions depend in a Borel--measurable way on the initial data. In particular, they are almost continuously dependent on the initial data. |
| title | Well-posedness of the Euler system of gas dynamics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.18267 |