On the Stability of Self-similar Blow-up for $C^{1,\alpha}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$

Tarek M. Elgindi; Tej-Eddine Ghoul; Nader Masmoudi

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arXiv · 1910.14071

On the Stability of Self-similar Blow-up for $C^{1,\alpha}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$

Tarek M. Elgindi·Tej-Eddine Ghoul·Nader Masmoudi

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Abstract

We study the stability of recently constructed self-similar blow-up 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.

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Tarek M. Elgindi, Tej-Eddine Ghoul, Nader Masmoudi. 2019-10-30. On the Stability of Self-similar Blow-up for $C^{1,\alpha}$ Solutions to the Incompressible Euler Equations on $\mathbb{R}^3$. https://arxiv.org/abs/1910.14071

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