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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.06629 |
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| _version_ | 1866914146199535616 |
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| author | Gui, Changfeng Lai, Shanfa Liu, Yong Wei, Juncheng Yang, Wen |
| author_facet | Gui, Changfeng Lai, Shanfa Liu, Yong Wei, Juncheng Yang, Wen |
| contents | This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a non-variational Lyapunov-Schmidt reduction in [26], are not energy minimizers and thus require a direct stability analysis. We adapt the Grillakis-Shatah-Strauss framework within Mielke's approach to handle the mismatch between well-posedness and energy spaces. The proof relies on spectral analysis of the linearized dynamics and careful treatment of the Hamiltonian structure defined by the energy and momentum functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions Gui, Changfeng Lai, Shanfa Liu, Yong Wei, Juncheng Yang, Wen Analysis of PDEs This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a non-variational Lyapunov-Schmidt reduction in [26], are not energy minimizers and thus require a direct stability analysis. We adapt the Grillakis-Shatah-Strauss framework within Mielke's approach to handle the mismatch between well-posedness and energy spaces. The proof relies on spectral analysis of the linearized dynamics and careful treatment of the Hamiltonian structure defined by the energy and momentum functionals. |
| title | Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.06629 |