Finite Time Singularities to the 3D Incompressible Euler Equations for Solutions in C∞(R3 \ {0}) ∩ C1,α ∩ L2
We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-f...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2025 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/422704 |
| Online Access: | http://hdl.handle.net/10261/422704 https://api.elsevier.com/content/abstract/scopus_id/105010061559 |
| Access Level: | Open access |
| Keyword: | Euler equations Incompressible fluids Singularities |
| Summary: | We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in R3 × [−T, 0] such that the velocity is in the space C∞(R3 \ {0}) ∩ C1,α ∩ L2 where 0 < α ≪ 1 for times t ∈ (−T, 0) and is not C1 at time 0. |
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