Two-dimensional water waves with constant vorticity and general bottom topography
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908373241298944 |
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| author | Pasquali, S. |
| author_facet | Pasquali, S. |
| contents | In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes the one by Zakharov-Craig-Sulem for irrotational water waves, and the one by Constantin-Ivanov-Prodanov for water waves with constant vorticity and flat bottom topography. We study in detail an operator which appears in such formulation, extending well-known results for the classical Dirichlet-Neumann operator, such as an analiticity result, the Taylor expansion in homogeneous powers of the wave profile, and a paralinearization formula. As an application, we prove a local well-posedness result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-dimensional water waves with constant vorticity and general bottom topography Pasquali, S. Analysis of PDEs 37K45, 76B03, 76B15 In this paper we consider two-dimensional water waves with constant vorticity, under the action of gravity and surface tension, in a fluid domain with finite depth and general bottom topography. We present a formulation which generalizes the one by Zakharov-Craig-Sulem for irrotational water waves, and the one by Constantin-Ivanov-Prodanov for water waves with constant vorticity and flat bottom topography. We study in detail an operator which appears in such formulation, extending well-known results for the classical Dirichlet-Neumann operator, such as an analiticity result, the Taylor expansion in homogeneous powers of the wave profile, and a paralinearization formula. As an application, we prove a local well-posedness result. |
| title | Two-dimensional water waves with constant vorticity and general bottom topography |
| topic | Analysis of PDEs 37K45, 76B03, 76B15 |
| url | https://arxiv.org/abs/2505.05430 |