Singularity formation for some incompressible Euler flows

Analysis Seminar
Topic:Singularity formation for some incompressible Euler flows
Speaker:Tarek Elgindi
Affiliation:University of California, San Diego
Date:Monday, May 6
Time/Room:3:00pm - 4:00pm/Simonyi Hall 101

We describe a recent construction of self-similar blow-up solutions of the incompressible Euler equation. A consequence of the construction is that there exist finite-energy $C^{1,a}$ solutions to the Euler equation which develop a singularity in finite time for some range of $a>0$. The approach we follow is to isolate a simple non-linear equation which encodes the leading order dynamics of solutions to the Euler equation in some regimes and then prove that the simple equation has stable self-similar blow-up solutions.