Global weak solutions of the Serre-Green-Naghdi equations with surface tension
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909127370866688 |
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| author | Guelmame, Billel |
| author_facet | Guelmame, Billel |
| contents | We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an $H^1$-equivalent energy. We prove the existence of global weak dissipative solutions for any relatively small-energy initial data. We also prove that the Riemann invariants of the solutions satisfy a one-sided Oleinik inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global weak solutions of the Serre-Green-Naghdi equations with surface tension Guelmame, Billel Analysis of PDEs We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an $H^1$-equivalent energy. We prove the existence of global weak dissipative solutions for any relatively small-energy initial data. We also prove that the Riemann invariants of the solutions satisfy a one-sided Oleinik inequality. |
| title | Global weak solutions of the Serre-Green-Naghdi equations with surface tension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.02214 |