Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916838795902976 |
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| author | Pasquali, S. |
| author_facet | Pasquali, S. |
| contents | In this paper we consider three-dimensional water waves with vorticity, under the action of gravity. We discuss a generalized Zakharov-Craig-Sulem formulation of the problem introduced by Castro and Lannes, which involves a generalized Dirichlet-Neumann operator. We study this operator in detail, extending some well-known results about the classical Dirichlet-Neumann operator for irrotational water waves, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and a paralinearization result. We stress the fact that no geometric condition on either the velocity field or the vorticity is assumed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity Pasquali, S. Analysis of PDEs 37K45, 76B03, 76B15 In this paper we consider three-dimensional water waves with vorticity, under the action of gravity. We discuss a generalized Zakharov-Craig-Sulem formulation of the problem introduced by Castro and Lannes, which involves a generalized Dirichlet-Neumann operator. We study this operator in detail, extending some well-known results about the classical Dirichlet-Neumann operator for irrotational water waves, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and a paralinearization result. We stress the fact that no geometric condition on either the velocity field or the vorticity is assumed. |
| title | Analytical study of a generalized Dirichlet-Neumann operator for three-dimensional water waves with vorticity |
| topic | Analysis of PDEs 37K45, 76B03, 76B15 |
| url | https://arxiv.org/abs/2502.09370 |