Nearly parallel helical vortex filaments in the three dimensional Euler equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912231206158336 |
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| author | Guerra, Ignacio Musso, Monica |
| author_facet | Guerra, Ignacio Musso, Monica |
| contents | Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids. In this study, we rigorously justify this model for two configurations: the central configuration consisting of regular polygons of $N$ helical-filaments rotating with constant speed, and the central configurations of $N+1$ vortex filaments, where an $N$-polygonal central configuration surrounds a central straight filament. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nearly parallel helical vortex filaments in the three dimensional Euler equations Guerra, Ignacio Musso, Monica Analysis of PDEs Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids. In this study, we rigorously justify this model for two configurations: the central configuration consisting of regular polygons of $N$ helical-filaments rotating with constant speed, and the central configurations of $N+1$ vortex filaments, where an $N$-polygonal central configuration surrounds a central straight filament. |
| title | Nearly parallel helical vortex filaments in the three dimensional Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2502.01470 |