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arXiv · 2602.17570

On putative self-similarity for incompressible 3D Euler

Peter Constantin·Mihaela Ignatova·Vlad Vicol
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Abstract

We consider hypothetical solutions of 3D Euler which blow up in finite time in a self-similar fashion. We prove that if the initial data has finite kinetic energy, then the similarity exponent $\gamma$ which governs the rate of zooming in must be at least $2/5$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $\gamma \geq 1/2$. For axisymmetric solutions, we establish the bound $\gamma\geq 1/2$ under the sole assumption that the velocity profile is $C^2$ smooth.

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Peter Constantin, Mihaela Ignatova, Vlad Vicol. 2026-02-19. On putative self-similarity for incompressible 3D Euler. https://arxiv.org/abs/2602.17570

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