Finite-time singularity formation for $C^{1,\alpha }$ solutions to the incompressible Euler equations on $\mathbb{R}^3$

Pages 647-727 from Volume 194 (2021), Issue 3 by Tarek M. Elgindi

Abstract

It has been known since work of Lichtenstein and Gunther in the 1920s 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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Keywords
, ,
Mathematical Subject Classification
Primary:
DOI
https://doi.org/10.4007/annals.2021.194.3.2
MR
4334974
zbMATH
7441733
Milestones
Received: 29 April 2019
Revised: 2 August 2021
Accepted: 16 August 2021
Published online: 2 November 2021

Authors

Tarek M. Elgindi

University of California, San Diego, La Jolla, CA

Current address:

Duke University, Durham, NC