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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/2507.16474 |
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| _version_ | 1866916856163467264 |
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| author | Abe, Ken Jeong, In-Jee Yao, Yao |
| author_facet | Abe, Ken Jeong, In-Jee Yao, Yao |
| contents | In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the solution. The strategy of the proof is robust, and we present several potential extensions of the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability for multiple Lamb dipoles Abe, Ken Jeong, In-Jee Yao, Yao Analysis of PDEs Mathematical Physics In the class of nonnegative vorticities on the half-plane, we establish the Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that the dipoles are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the solution. The strategy of the proof is robust, and we present several potential extensions of the result. |
| title | Stability for multiple Lamb dipoles |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2507.16474 |