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Friday, June 07, 2019
4:00 PM - 5:00 PM
Linde Hall 310

Special Math Colloquium

Singularity formation for incompressible Euler flows
Tarek Elgindi, Department of Mathematics, UC San Diego,

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 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. This builds off of previous work with I. Jeong and with T. Ghoul and N. Masmoudi.

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