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 larger than $\frac{2}{5}$. If a smooth globally self-similar blowup profile exists, and this profile satisfies an outgoing property, we prove that $\gamma \ge \frac{1}{2}$. For axisymmetric solutions, we establish the bound $\gamma \ge \frac{1}{2}$ under the sole assumption that the velocity profile is $C^2$ smooth.

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