# Analysis Seminar

#### Singularity formation for some incompressible Euler flows

**Speaker:**
Tarek Elgindi, UCSD

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, September 5, 2019, 11 a.m.

**Synopsis:**

We describe a recent construction of self-similar blow-up solutions

for the incompressible Euler equation. A consequence of the

construction is that there exist finite-energy $C^{1,a}$ solutions to

the Euler equation that develop a singularity in finite time for some

range of $a>0$. The approach we follow is to isolate a simple

non-linear equation that encodes the leading order dynamics of

solutions to the Euler equation in some regimes and then prove that

the simplified equation has stable self-similar blow-up solutions.

The talk will include results based on some joint works with I. Jeong

and T. Ghoul and N. Masmoudi.