S4B2 - Graduate Seminar in Analysis and PDEs - Topics in Incompressible Fluid Dynamics
Winter term 2024/2025
Organisational details
- Time: Thursday. Place: Endenicher Allee 60 - SemR 0.007
- Second preliminary meeting: Thursday 10.10.2024, 16:00 (in the normal room). We will give a summary presentation of the topic and the articles, and proceed to the distribution of topics. (there still are many open slots!) If you cannot attend, please contact the organizer to get an appointment.
- If there are any questions, please get in touch with the organiser. If you are a participating Masters student, please register on Basis.
Overview
This seminar series are centered on the study of the Euler and Navier-Stokes equations, and the properties of their solutions. We will first start by covering the classical question of existence and uniqueness of solutions for a given initial datum. This will involve getting familiar with important tools from harmonic analysis. However, the analysis of these PDEs goes much deeper than the (already fascinating) existence/uniqueness problems: we will also examine some important properties of the solutions. For example, we will study the asymptotic behavior of solutions at large space scales, mixing properties and the growth of higher order norms, point vortex dynamics, or the distribution of kinetic energy in the solutions. Other related models such as magnetohydrodynamics will also recieve some attention.
See here for more information, including a list of literature recommendations.
Prerequisites: basic knowledge of Fourier series and transform, functional analysis, Sobolev spaces and ODEs. No prior experience in physics is required.
Schedule of talks
This is an approximate schedule. The order of the talks may vary depending on the topics that are chosen.
October 10- Preliminary meeting
October 17- Weak Leray Solutions for the Navier-Stokes Equations Taken
October 24- Strong Solutions for the Navier-Stokes Equations in Sobolev Spaces Taken
October 31- Strong Solutions for the Navier-Stokes Equations in Lebesgue Spaces Taken
November 7- Hexagonal Structure in the 2D Navier-Stokes Flow Taken
November 14- No Seminar (Rescheduled to...)
November 21- Yudovich Solutions for the 2D Euler Equations Taken
November 28- Transport and Instability for Perfect Fluids Taken
December 5- No seminar (rescheduled to...)
December 12- Point Vortex Solutions for the 2D Euler Equations Taken
December 19- Uniqueness for the Vortex-Wave System when the Vorticity is Constant Near the Point Vortex TBA
December 26- Christmas break
January 2- Christmas break
January 9- Maximal Regularity and the 2D inviscid MHD Equations TBA
January 16- Infinite Energy Solutions of the Two-Dimensional Navier-Stokes Equations TBA
January 23- Stability of Vortices in Ideal Fluids TBA
News
04.11.24: Hirzebruch lecture by Lisa Sauermann
Gerd Faltings elected member of the Order Pour le MÃ©rite
Geordie Williamson receives the Max Planck-Humboldt Research Award 2024
ERC Starting Grant for Markus Hausmann
EMS Prize 2024 for Jessica Fintzen
Bonn mathematics performs excellently again in QS ranking
Stefan Schwede is invited speaker at the ECM 2024 in Sevilla
Jessica Fintzen wins Cole Prize
Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Peter Scholze elected as Foreign Member of the Royal Society