On the gravity-capillary water waves with point vortices
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910918635421696 |
|---|---|
| author | Wan, Lizhe |
| author_facet | Wan, Lizhe |
| contents | We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water wave system has a unique solution for initial data in $\mathcal{H}^s\times Ω_t^N$, $s>\frac{3}{2}$. Finally, we show that if there are only two vortices, and vortices, initial velocity, and initial surfaces are symmetric with respect to the vertical axis, then the solution of pure capillary water waves with two point vortices has an extended cubic lifespan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the gravity-capillary water waves with point vortices Wan, Lizhe Analysis of PDEs 35Q31, 76B03, 76B47 We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water wave system has a unique solution for initial data in $\mathcal{H}^s\times Ω_t^N$, $s>\frac{3}{2}$. Finally, we show that if there are only two vortices, and vortices, initial velocity, and initial surfaces are symmetric with respect to the vertical axis, then the solution of pure capillary water waves with two point vortices has an extended cubic lifespan. |
| title | On the gravity-capillary water waves with point vortices |
| topic | Analysis of PDEs 35Q31, 76B03, 76B47 |
| url | https://arxiv.org/abs/2504.17951 |