On putative self-similarity for incompressible 3D Euler

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.