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

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arxiv 1910.14071 v1 pith:FSELX33Y submitted 2019-10-30 math.AP physics.flu-dyn

Tarek M. Elgindi , Tej-Eddine Ghoul , Nader Masmoudi This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords solutionsalphaself-similarblow-upeulerincompressiblestabilitybeale-kato-majda
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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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  1. Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity

    math.AP 2026-07 unverdicted novelty 2.0 of 10

    Analytic low-rank corrections convert numerically determined global basis functions into exactly vanishing local modes, enforcing |x|^3 vanishing conditions needed for singular weighted stability estimates in computer...

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