Finite-Time Singularity Formation for C^1,α Solutions to the Incompressible Euler Equations on ℝ³

2019/04/09 by Tarek M. Elgindi, Elgindi, Tarek M. · 5 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1904.04795

openalex publication_date 2019/04/09 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

It has been known since work of Lichtenstein [42] and Gunther [29] in the 1920's that the 3D incompressible Euler equation is locally well-posed in the class of velocity fields with Hölder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.

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Related

• Finite time singularities to the 3D incompressible Euler equations for solutions in C^∞(ℝ³ ∖ \0\)∩ C^1,α∩ L²
• Finite-time Singularity Formation for Strong Solutions to the 3D Euler equations, II
• Finite-time Singularity Formation for Strong Solutions to the 3D Euler Equations, I
• Incompressible Euler Equations: the blow-up problem and related results
• Singularity formation in the incompressible Euler equation in finite and infinite time