Existence of stationary vortex patches for the gSQG in bounded domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910444190433280 |
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| author | Angulo-Castillo, Vladimir Cuba, Edison Ferreira, Lucas C. F. |
| author_facet | Angulo-Castillo, Vladimir Cuba, Edison Ferreira, Lucas C. F. |
| contents | In this paper we show the existence of time-periodic vortex patches for the generalized surface quasi-geostrophic equation within a bounded domain. This construction is carried out for values of $γ$ in the range of $(1,2)$. The resulting vortex patches possess a fixed vorticity and total flux, and they are located in the neighborhood of critical points that are non-degenerate for the Kirchhoff--Routh equation. The proof is accomplished through a combination of analyzing the linearization of the contour dynamics equation and employing the implicit function theorem as well as carefully selected function spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_07427 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of stationary vortex patches for the gSQG in bounded domains Angulo-Castillo, Vladimir Cuba, Edison Ferreira, Lucas C. F. Analysis of PDEs 35Q35, 76B47, 76B03 In this paper we show the existence of time-periodic vortex patches for the generalized surface quasi-geostrophic equation within a bounded domain. This construction is carried out for values of $γ$ in the range of $(1,2)$. The resulting vortex patches possess a fixed vorticity and total flux, and they are located in the neighborhood of critical points that are non-degenerate for the Kirchhoff--Routh equation. The proof is accomplished through a combination of analyzing the linearization of the contour dynamics equation and employing the implicit function theorem as well as carefully selected function spaces. |
| title | Existence of stationary vortex patches for the gSQG in bounded domains |
| topic | Analysis of PDEs 35Q35, 76B47, 76B03 |
| url | https://arxiv.org/abs/2405.07427 |