November 2021 Finite-time singularity formation for $C^{1,\alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^3$
Tarek M. Elgindi
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Ann. of Math. (2) 194(3): 647-727 (November 2021). DOI: 10.4007/annals.2021.194.3.2

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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Tarek M. Elgindi. "Finite-time singularity formation for $C^{1,\alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^3$." Ann. of Math. (2) 194 (3) 647 - 727, November 2021. https://doi.org/10.4007/annals.2021.194.3.2

Information

Published: November 2021
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2021.194.3.2

Subjects:
Primary: 35Q31

Keywords: asymptotic stability , Euler equations , singularity formation

Rights: Copyright © 2021 Department of Mathematics, Princeton University

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Vol.194 • No. 3 • November 2021
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