On putative self-similarity for incompressible 3D Euler

2026/02/19 by Peter Constantin, Mihaela Ignatova, Vlad Vicol · 1 citation
#math.AP

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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 γ 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 γ≥ 1/2. For axisymmetric solutions, we establish the bound γ≥ 1/2 under the sole assumption that the velocity profile is C² smooth.

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• Self-Similar Solutions of the Two-Dimensional Incompressible Euler Equation from Large Initial Data

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