| Lecture | Time | Place | ZoomLink |
|---|---|---|---|
| Lecture 1 | 10:45-12:15, 16.06.2025 | Main Lecture Hall, Ex-Isef | |
| Lecture 2 | 14:15-15:45, 18.06.2025 | Main Lecture Hall, Ex-Isef | |
| Lecture 3 | 10:45-12:15, 17.06.2025 | Main Lecture Hall, Ex-Isef | |
| Lecture 4 | 10:45-12:15, 19.06.2025 | Main Lecture Hall, Ex-Isef | |
| Office hours | 16:00-17:00, 19.06.2025 | Main Lecture Hall, Ex-Isef |
Date: 16 June 2025 - 20 June 2025
Abstract:
I will discuss several recent themes in research on regularity and small scale creation in equations of fluid mechanics and related PDE. I will start with the broad overview of the field, and then present some recent results on small scale creation in solutions of the incompressible porous media equation and some other models. I will also talk about possible suppression of singularity formation by fluid flow. I will focus on the case of the Keller-Segel equation that describes chemotaxis, and is perhaps the most studied model of mathematical biology. The next topic will be dynamics of vortex and SQG patches. Patches are a special class of solutions for which dynamics reduces to evolution of a curve. I will talk about possible singularity formation and recent ill-posedness results. Finally, if time permits, I will discuss the method of modulus of continuity for showing global regularity of solutions to fluid mechanics PDE, and its recent application to an equation proposed by Steinerberger in connection with describing the evolution of polynomial roots under differentiation.