Cambridge Journal of Mathematics

Volume 9 (2021)

Number 4

On the stability of self-similar blow-up for $C^{1,\alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^3$

Pages: 1035 – 1075

DOI: https://dx.doi.org/10.4310/CJM.2021.v9.n4.a4

Authors

Tarek M. Elgindi (Department of Mathematics, University of California, San Diego, Calif., U.S.A.)

Tej-Eddine Ghoul (Department of Mathematics, New York University Abu-Dhabi, United Arab Emirates)

Nader Masmoudi (Department of Mathematics, New York University Abu-Dhabi, United Arab Emirates; and Courant Institute of Mathematical Sciences, New York University, N.Y., U.S.A.)

Abstract

We study the stability of recently constructed self-similar blowup solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{1,\alpha}$ solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale–Kato–Majda criterion cannot be improved in the class of $C^{1,\alpha}$ solutions.

Full Text (PDF format)

Received 19 March 2020

Published 22 March 2022