Rigidity of symmetric doubly-periodic water waves near shear flows
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910921607086080 |
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| author | Seth, Douglas Svensson Varholm, Kristoffer Wahlén, Erik Weber, Jörg |
| author_facet | Seth, Douglas Svensson Varholm, Kristoffer Wahlén, Erik Weber, Jörg |
| contents | We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform background flows, where the existence of truly three-dimensional bifurcating waves is well known. While this paper focuses on capillary-gravity water waves, our proof also applies to other suitable types of dynamic boundary conditions, such as hydroelastic waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of symmetric doubly-periodic water waves near shear flows Seth, Douglas Svensson Varholm, Kristoffer Wahlén, Erik Weber, Jörg Analysis of PDEs 76B15, 76B03, 35Q35, 35Q31 We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform background flows, where the existence of truly three-dimensional bifurcating waves is well known. While this paper focuses on capillary-gravity water waves, our proof also applies to other suitable types of dynamic boundary conditions, such as hydroelastic waves. |
| title | Rigidity of symmetric doubly-periodic water waves near shear flows |
| topic | Analysis of PDEs 76B15, 76B03, 35Q35, 35Q31 |
| url | https://arxiv.org/abs/2504.20221 |