Dissipative Euler flows originating from circular vortex filaments
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910399881805824 |
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| author | Gancedo, Francisco Hidalgo-Torné, Antonio Mengual, Francisco |
| author_facet | Gancedo, Francisco Hidalgo-Torné, Antonio Mengual, Francisco |
| contents | In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in $C([0,T],L^{2^-})$. The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dissipative Euler flows originating from circular vortex filaments Gancedo, Francisco Hidalgo-Torné, Antonio Mengual, Francisco Analysis of PDEs 76B03 In this paper, we prove the first existence result of weak solutions to the 3D Euler equation with initial vorticity concentrated in a circle and velocity field in $C([0,T],L^{2^-})$. The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and moves in the direction of the symmetry axis. With our approach, there is no need to mollify the initial data or to rescale the time variable. We overcome the singularity of the initial data by applying convex integration within the appropriate time-weighted space. |
| title | Dissipative Euler flows originating from circular vortex filaments |
| topic | Analysis of PDEs 76B03 |
| url | https://arxiv.org/abs/2404.04250 |