Séminaire Analyse non linéaire et EDP

We discuss constraints on hypothetical finite-time (backwards) self-similar blow-up solutions for solutions of incompressible Euler and incompressible Navier-Stokes on R^3. In various situations, we show that the very existence of a smooth similarity profile imposes strong restrictions on the similarity exponent. We also discuss new Liouville-type theorems for the viscous problem.