V5B2 - Selected Topics in Analysis and PDEs - Dispersive PDEs: deterministic and probabilistic perspectives
Summer term 2024/2025
Organisational details
- Time and place: Friday 10h-12h, SemR 1.008
- If there are any questions, please get in touch with the lecturer. If you are a participating Masters student, please register on Basis.
Overview
The lecture aims to provide the basics of dispersive partial differential equations (PDEs) from both an analytic point of view and also a probabilistic point of view. Dispersive PDEs are a class of PDEs where different frequencies propagate at different velocities. We shall mainly use Schrödinger equations and wave equations as examples and use tools from harmonic analysis and probability theory to study well-posedness (existence, uniqueness, and stability under perturbation) of these equations.
The lecture is divided into two main parts. In the first part of the lecture, we discuss deterministic well-posedness theory of nonlinear Schrödinger equations and nonlinear wave equations. A highlight of this part is the Strichartz estimates which allow us to show well-posedness in (sub-)critical regimes. In the second part, we discuss probabilistic well-posedness theory of nonlinear Schrödinger equations and nonlinear wave equations using the randomized initial data, which goes beyond deterministic well-posedness results.
Practical Details
The syllabus contains additional details, including a list of prerequisites, a tentative schedule and literature recommendations.
News
Daniel Huybrechts elected as member of Leopoldina
Catharina Stroppel appointed Honorary Doctor at Uppsala University
Angkana Rüland receives Gottfried Wilhelm Leibniz Prize 2025
Wolfgang Lück receives the von Staudt Prize
Gerd Faltings elected member of the Order Pour le Mérite
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