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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2024
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| Accès en ligne: | https://arxiv.org/abs/2402.15261 |
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| _version_ | 1866917603484631040 |
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| author | Guelmame, Billel Clamond, Didier Junca, Stéphane |
| author_facet | Guelmame, Billel Clamond, Didier Junca, Stéphane |
| contents | Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh. This system is Galilean invariant, linearly non-dispersive and conserves formally an $H^1$-like energy. In this paper, we generalise this regularisation for the barotropic Euler system preserving the same properties. We prove the local (in time) well-posedness of the regularised barotropic Euler system and a periodic generalised two-component Hunterr-Saxton system. We also show for both systems that if singularities appear in finite time, they are necessary in the first derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian regularisation of the unidimensional barotropic Euler equations Guelmame, Billel Clamond, Didier Junca, Stéphane Analysis of PDEs Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh. This system is Galilean invariant, linearly non-dispersive and conserves formally an $H^1$-like energy. In this paper, we generalise this regularisation for the barotropic Euler system preserving the same properties. We prove the local (in time) well-posedness of the regularised barotropic Euler system and a periodic generalised two-component Hunterr-Saxton system. We also show for both systems that if singularities appear in finite time, they are necessary in the first derivatives. |
| title | Hamiltonian regularisation of the unidimensional barotropic Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.15261 |