Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911582908317696 |
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| author | Averkiou, Averkios Musso, Monica Yu, Fang |
| author_facet | Averkiou, Averkios Musso, Monica Yu, Fang |
| contents | We consider the three-dimensional incompressible Euler equations for helical flows without swirl. By adapting gluing techniques, we construct the first smooth multi-vortex solution in the whole space $\mathbb{R}^3$ exhibiting a cluster of collapsing helical filaments, with the associated cross-sectional vorticity remaining compactly supported in $\mathbb{R}^2$ for all times. Our result generalises previous collapsing configurations in $\mathbb{R}^3$ with rapidly decaying vorticity cores, and extends related variational solutions obtained in infinite cylindrical domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations Averkiou, Averkios Musso, Monica Yu, Fang Analysis of PDEs We consider the three-dimensional incompressible Euler equations for helical flows without swirl. By adapting gluing techniques, we construct the first smooth multi-vortex solution in the whole space $\mathbb{R}^3$ exhibiting a cluster of collapsing helical filaments, with the associated cross-sectional vorticity remaining compactly supported in $\mathbb{R}^2$ for all times. Our result generalises previous collapsing configurations in $\mathbb{R}^3$ with rapidly decaying vorticity cores, and extends related variational solutions obtained in infinite cylindrical domains. |
| title | Clustered vortex helices with compactly supported cross-sectional vorticity in the 3D Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.09546 |