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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2307.05573 |
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| _version_ | 1866916099295019008 |
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| author | Kozlov, Vladimir |
| author_facet | Kozlov, Vladimir |
| contents | We consider Stokes water waves on the vorticity flow in a two-dimensional channel of finite depth. In the paper "V.Kozlov, On first subharmonic bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence of subharmonic bifurcations on a branch of Stokes waves. Such bifurcations occur near the first bifurcation in the set of Stokes waves. Moreover it is shown in that paper that the bifurcating solutions build a connected continuum containing large amplitude waves. This fact was proved under a certain assumption concerning the second eigenvalue of the Frechet derivative. In this paper we investigate this assumption and present explicit conditions when it is satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05573 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the first bifurcation of Stokes waves Kozlov, Vladimir Analysis of PDEs We consider Stokes water waves on the vorticity flow in a two-dimensional channel of finite depth. In the paper "V.Kozlov, On first subharmonic bifurcations in a branch of Stokes waves, JDE, 2024," it was proved existence of subharmonic bifurcations on a branch of Stokes waves. Such bifurcations occur near the first bifurcation in the set of Stokes waves. Moreover it is shown in that paper that the bifurcating solutions build a connected continuum containing large amplitude waves. This fact was proved under a certain assumption concerning the second eigenvalue of the Frechet derivative. In this paper we investigate this assumption and present explicit conditions when it is satisfied. |
| title | On the first bifurcation of Stokes waves |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.05573 |