Dissipative Euler Flows Originating from Circular Vortex Filaments
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], L2-). The energy becomes finite and decreasing for positive times, with vorticity concentrated in a ring that thickens and mov...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/181745 |
| Acceso en línea: | https://hdl.handle.net/11441/181745 https://doi.org/10.1007/s40818-025-00211-5 |
| Access Level: | acceso abierto |
| Palabra clave: | Incompressible fluid Euler equations Navier-Stokes Vortex filaments Convex integration Axial symmetry |
| Sumario: | 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], L2-). 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. |
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