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...

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Detalles Bibliográficos
Autores: Córdoba, Diego, Martinez-Zoroa, Luis, Zheng, Fan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/422704
Acceso en línea:http://hdl.handle.net/10261/422704
https://api.elsevier.com/content/abstract/scopus_id/105010061559
Access Level:acceso abierto
Palabra clave:Euler equations
Incompressible fluids
Singularities
Descripción
Sumario: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.