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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.15176 |
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| _version_ | 1866912130919301120 |
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| author | Sakajo, Takashi Zou, Changjun |
| author_facet | Sakajo, Takashi Zou, Changjun |
| contents | We construct a series of classic vorticity solutions for incompressible Euler equation on $\mathbb S^2$, which constitute the $C^1$ type regularization for a general traveling point vortex system. The construction is accomplished by applying tangent mapping on $\mathbb S^2$ and Lyapunov--Schmidt reduction argument. Using the fixed-point theorem and a finite dimensional equation on vortex dynamics, we prove that the vortices are located near a nondegenerate critical point of Kirchhoff--Routh function. Moreover, in the tangent space at each vortex center, the scaled stream function is verified as a perturbation of the ground state for generalized plasma problem. Some other qualitative and quantitative estimates for the regularization series are also obtained in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15176 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $C^1$ type regularization for point vortices on $\mathbb S^2$ Sakajo, Takashi Zou, Changjun Analysis of PDEs 76B47 We construct a series of classic vorticity solutions for incompressible Euler equation on $\mathbb S^2$, which constitute the $C^1$ type regularization for a general traveling point vortex system. The construction is accomplished by applying tangent mapping on $\mathbb S^2$ and Lyapunov--Schmidt reduction argument. Using the fixed-point theorem and a finite dimensional equation on vortex dynamics, we prove that the vortices are located near a nondegenerate critical point of Kirchhoff--Routh function. Moreover, in the tangent space at each vortex center, the scaled stream function is verified as a perturbation of the ground state for generalized plasma problem. Some other qualitative and quantitative estimates for the regularization series are also obtained in this paper. |
| title | $C^1$ type regularization for point vortices on $\mathbb S^2$ |
| topic | Analysis of PDEs 76B47 |
| url | https://arxiv.org/abs/2411.15176 |