Reading seminar (Spring 2020): Finite time singularity formation in incompressible fluids

The goal of this reading seminar is to study the recent remarkable work of T. Elgindi on the construction of finite time singularity formation for the incompressible Euler equation. I am planning to go at a leisurely pace so that everybody can follow (well, at least in the beginning!).


In general, we will meet on Wednesdays from 4 pm to 5 pm in Evans 748 (see the syllabus below for the precise schedule).

Update (3/9): Due to the current situation with the coronavirus, we will cancel all in-person meetings in March (which may be extended until later).

Update (4/22): After a long hiatus, we will to continue the reading seminar on Zoom.

Syllabus (tentative)
Date Topic Speaker
2/19 (Place: Evans 887) Organizational meeting
2/26 No meeting (I'll be away).
3/4 (SPECIAL TIME: 5 pm - 6 pm) Local well-posedness of the incompressible Euler equations: $L^2$ Sobolev spaces, Hölder spaces Mohandas Pillai
3/11 (MEETING CANCELLED) Beale-Kato-Majda theorem, global existence of regular axi-symmetric flows without swirl
Notes: pdf
Benjamin Pineau
3/18 (MEETING CANCELLED) T. Elgindi and I.-J. Jeong. Ill-posedness for the Incompressible Euler equations in critical Sobolev spaces (a nice short paper that can be served as an introduction to the hyperbolic flow configuration à la Kiselev-Sverak, which is also crucially used in Elgindi's construction) Mitchell Taylor
3/25 No meeting (spring break)
4/1 No meeting
4/8 No meeting
4/15 No meeting
4/22 T. Elgindi and I.-J. Jeong, On the Effects of Advection and Vortex Stretching (construction of finite-time blow-up for the De Gregorio model, which is a simplified 1d model for incompressible Euler) Thibault de Poyferré
4/29 T. Elgindi. Finite-time singularity formation for $C^{1, \alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^{3}$ (the main paper of this seminar) Slides: pdf Sung-Jin Oh
5/6 T. Elgindi, T.-E. Ghoul and N. Masmoudi. (stability of the self-similar blow-up solution constructed above, and in particular, existence of a finite energy finite time blow-up solution) Georgios Moschidis
References (for background and for the first two topics)
1 J.-Y. Chemin, Perfect incompressible fluids
2 A. Majda and A. Bertozzi, Vorticity and incompressible flow
3 T. Tao, Lecture notes for Math 254A (incompressible fluid equations) and 255B (incompressible Euler equations)

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