| 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!). |
| Schedule |
| 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 |