Undergraduate Seminar "Partielle Differentialgleichungen und ihre Anwendungen" (German)
Graduate Seminar "Topics in Mathematical Fluid Dynamics"
Advanced Graduate Seminar "Advanced Topics in Analysis & PDEs"
In this lecture, we will develop classic harmonic analysis tools for partial differential equations. The topics are:
Fourier Transformations, Fourier Series
Hardy-Littlewood maximal functions
Hardy and BMO spaces
This lecture is a continuation of a standard introductory course in partial differential equations. Necessary basic knowlege of partial differential equations can be also be acquired during the semester.
Partielle Differentialgleichungen und ihre Anwendungen
In diesem Bachelor-Seminar beschäftigen wir uns mit elementaren Problemen im Bereich partieller Differentialgleichungen, sowie ersten Anwendungen der mathematischen Theorie auf Probleme der Physik. Grundlegende Kenntnisse von Partiellen Differentialgleichungen sind erwünscht; diese können aber auch parallel zum Seminar erworben werden.
Das Seminar kann auf eine Bachelorarbeit in diesem Gebiet vorbereiten.
Bei Interesse, kontaktieren Sie uns gerne via Email: email@example.com
Topics in Mathematical Fluid Dynamics
This graduate seminar is intended for students in the Master's programs in Mathematics or Physics.
Depending on the background of the participants, we will discuss basic concepts or feasible research papers in the mathematical theory of fluid dynamics. Participating students should be familiar with partial differential equations on the level of a standard introductory course (e.g., PDGL 1).
The Seminar can lead to a Master's thesis.
Interested students should contact us by email firstname.lastname@example.org
Advanced Topics in ANALYSIS & PDEs
This is a reading seminar that we run together with André Schlichting's group. It runs all year round. We read mathematical papers related to mixing and turbulence, transport and diffusion, or whatever looks interesting to (at least) one of us. Some papers are classics, some are brand new on the arXiv.
We meet currently on Mondays at 10:00. Interested? Then write us an email!
We start the new year with a focus on Random Dynamical Systems by reading Arnold's book. This will keep us busy for a few months... The first meeting is on Monday, Jan 31.
Here is an overview of past and future topics:
Nov 22, Dec 6 & 13: Víctor talks about the well-posedness of the 2D Navier-Stokes equations with measure-valued initial data
Oct 25, Nov 8 & 15: Domink describes an alternative approach to sharp extinction rates
Oct 8, 11 & 18: Christian presents a new work on sharp extinction rates for fast diffusions on bounded domains
June 30: Víctor presents his new work on stability estimates for advection-diffusion equations in the DiPerna-Lions setting and beyond
May 31, June 9 and 16: André speaks about the mean-field limit for Coulomb-type flows
April 30 & May 12: Dominik presents results on the large-time asymptotics for the thin film equation, its gradient flow interpretation and its relation to the porous medium equation
March 26, April 1 & 21: Stefano presents Schochet's paper on the Euler mean field limit
Feb 12, March 5, 12 & 19 : Christian gives an introduction on vortex sheets and reads the classical Delort paper on measure valued solutions to Euler
Jan 22, 29 & Feb 5-- HAPPY NEW YEAR 2021!! -- We resume our seminar with a talk on universal mixers. Víctor's speaking!
Dec 11 & 18: Dominik presents a paper on invariant manifolds for Navier-Stokes
Nov 20, 27 & Dec 4: Stefano presents his results on the vortex dynamics for viscous fluids
Oct 30, Nov 6 & 13: Christian speaks about large time asymptotic expansions for the porous medium equation and the role of the spectrum
Oct 16 & 23: Dominik talks about large time asymptotics for the porous medium equation via the entropy method
Oct 2 & 9: Víctor talks about integrability estimates for advection-diffusion equations and their optimality