On the dynamics of leapfrogging vortex rings
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908414381129728 |
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| author | Donati, Martin Hientzsch, Lars Eric Lacave, Christophe Miot, Evelyne |
| author_facet | Donati, Martin Hientzsch, Lars Eric Lacave, Christophe Miot, Evelyne |
| contents | The evolution of highly concentrated vorticity around rings in the three-dimensional axisymmetric Euler equations is studied in a regime for which the leapfrogging dynamics predicted by Helmholtz is expected to occur. We provide in this paper the first result deriving this phenomenon for a general class of initial data in the suitable regime. The singular interaction of rings requires significant improvements of weak and strong localization estimates obtained in prior works. Our method is based on the combination of a new variational argument and a recently introduced double iterative procedure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dynamics of leapfrogging vortex rings Donati, Martin Hientzsch, Lars Eric Lacave, Christophe Miot, Evelyne Analysis of PDEs Mathematical Physics 35Q31, 76B47, 37N10 The evolution of highly concentrated vorticity around rings in the three-dimensional axisymmetric Euler equations is studied in a regime for which the leapfrogging dynamics predicted by Helmholtz is expected to occur. We provide in this paper the first result deriving this phenomenon for a general class of initial data in the suitable regime. The singular interaction of rings requires significant improvements of weak and strong localization estimates obtained in prior works. Our method is based on the combination of a new variational argument and a recently introduced double iterative procedure. |
| title | On the dynamics of leapfrogging vortex rings |
| topic | Analysis of PDEs Mathematical Physics 35Q31, 76B47, 37N10 |
| url | https://arxiv.org/abs/2503.21604 |