Finite time singularities to the 3D incompressible Euler equations for solutions in C^∞(ℝ³ ∖ \0\)∩ C^1,α∩ L²

2023/08/23 by Diego Córdoba, Córdoba, Diego, Luis Martínez-Zoroa +3
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2308.12197

openalex publication_date 2023/08/23 · openalex created_date 2023/08/25 · openalex updated_date 2026/07/28

Abstract

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\)∩ C^1,α∩ L² for times t∈ (-T,0) and is not C¹ at time 0.

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