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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2602.20131 |
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| _version_ | 1866918351267168256 |
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| author | Guo, Dengjun Jeong, In-Jee Zhao, Lifeng |
| author_facet | Guo, Dengjun Jeong, In-Jee Zhao, Lifeng |
| contents | We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl.
For a broad class of initial data sharing only the macroscopic invariants with a thin vortex ring, we prove that the vorticity remains sharply concentrated and propagates along the symmetry axis with leading-order speed given by the Kelvin--Hicks formula, providing the first global-in-time validation of the vortex filament conjecture for a single vortex ring arising from generic initial data.
We further identify a universal filamentation mechanism driven by the competition between rapid core translation and slower local induction. This mechanism gives linear-in-time stretching of the vortex support under very general assumptions on the data, yielding dynamical instability of any thin vortex ring configurations in the $W^{2,\infty}$ norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20131 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global dynamics of a single vortex ring Guo, Dengjun Jeong, In-Jee Zhao, Lifeng Analysis of PDEs We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad class of initial data sharing only the macroscopic invariants with a thin vortex ring, we prove that the vorticity remains sharply concentrated and propagates along the symmetry axis with leading-order speed given by the Kelvin--Hicks formula, providing the first global-in-time validation of the vortex filament conjecture for a single vortex ring arising from generic initial data. We further identify a universal filamentation mechanism driven by the competition between rapid core translation and slower local induction. This mechanism gives linear-in-time stretching of the vortex support under very general assumptions on the data, yielding dynamical instability of any thin vortex ring configurations in the $W^{2,\infty}$ norm. |
| title | Global dynamics of a single vortex ring |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.20131 |