Analysis Seminar

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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.