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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Bibliographic Details
Authors: Córdoba, Diego, Martinez-Zoroa, Luis, Zheng, Fan
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
Description
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.