Amplitude bounds of steady rotational water waves
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910442365911040 |
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| author | Haziot, Susanna V. Strauss, Walter A. |
| author_facet | Haziot, Susanna V. Strauss, Walter A. |
| contents | We consider classical steady water waves with a free surface, a flat bottom and constant vorticity $γ$. In the adverse case $γ>0$ we prove that there is an absolute upper bound on the amplitude, independent of the physical constants, provided that $γ$ is sufficiently small. In any favorable case $γ\leq0$ we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as $γ$ tends to negative infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Amplitude bounds of steady rotational water waves Haziot, Susanna V. Strauss, Walter A. Analysis of PDEs Mathematical Physics We consider classical steady water waves with a free surface, a flat bottom and constant vorticity $γ$. In the adverse case $γ>0$ we prove that there is an absolute upper bound on the amplitude, independent of the physical constants, provided that $γ$ is sufficiently small. In any favorable case $γ\leq0$ we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as $γ$ tends to negative infinity. |
| title | Amplitude bounds of steady rotational water waves |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2405.06529 |