Variational Instability for Irrotational Water Waves in Finite Depth
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912242613616640 |
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| author | Kogelbauer, Florian |
| author_facet | Kogelbauer, Florian |
| contents | We prove variational instability for small-amplitude solutions to the periodic irrotational gravity water wave problem in finite depth. Our results are based on a reformation of the water wave problem as a pseudo-differential Euler-Lagrange equation together with the local existence theory of small-amplitude waves. We use a perturbative spectral analysis of the second-variation operator in combination with a Plotnikov transformation to show instability for non-trivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational Instability for Irrotational Water Waves in Finite Depth Kogelbauer, Florian Analysis of PDEs We prove variational instability for small-amplitude solutions to the periodic irrotational gravity water wave problem in finite depth. Our results are based on a reformation of the water wave problem as a pseudo-differential Euler-Lagrange equation together with the local existence theory of small-amplitude waves. We use a perturbative spectral analysis of the second-variation operator in combination with a Plotnikov transformation to show instability for non-trivial solutions. |
| title | Variational Instability for Irrotational Water Waves in Finite Depth |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.16698 |