Analysis Seminar

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On Putative Self-Similarity for Incompressible 3D Euler

Speaker: Vlad Vicol, New York University

Location: Warren Weaver Hall 1302

Date: Thursday, April 2, 2026, 11 a.m.

Synopsis:

We study hypothetical finite-time self-similar blow-up solutions to the 3D incompressible Euler equations. We prove that finite kinetic energy of the initial data implies the similarity exponent γ satisfies γ ≥ 2/5. If a smooth globally self-similar blow-up profile exists and satisfies an outgoing condition, then γ ≥ 1/2. For axisymmetric solutions, we prove γ ≥ 1/2 under more general assumptions, including cases without the outgoing condition. This is joint work with Peter Constantin and Mihaela Ignatova.