V5B8 - Selected Topics in Analysis - The vector field method and quasilinear wave equations
Summer Semester 2022
- Dr. Dongxiao Yu
- Instructor
Lectures
- Tue 12-14, Room 1.007, Endenicher Allee 60. See here for the current COVID policy for the Mathematics Center.
- Lectures may be held on Zoom occasionally.
Office hours
Tue 14-15, Room 2.005, Endenicher Allee 60. Or by appointment.
Topics
In this course we will study the lifespans of solutions to some special types of quasilinear wave equations with small, smooth and localized initial data. Using the so-called ''vector field method'', we will prove several global or almost global existence results for quasilinear wave equations.
The prerequisites include basic real analysis and basic knowledge about partial differential equations.
Here is a tentative schedule.
- A review on the linear wave equation. (1.5 weeks)
- Energy estimates. (1.5 weeks)
- Local wellposedness and blowup criteria. (1 week)
- Commuting vector fields and some related inequalities. (2 weeks)
- An almost global existence result. (2 weeks)
- The null condition and a global existence result. (4 weeks)
Literature
Here are the lecture notes.
The following four books are recommended but not required:
- Christopher Sogge, Lectures on Non-Linear Wave Equations (Second Edition).
- Lars Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations.
- Serge Alinhac, Geometric Analysis of Hyperbolic Differential Equations: An Introduction.
- Serge Alinhac, Hyperbolic Partial Differential Equations.
My plan is to follow Chapter I and II in Sogge’s book and use the other three books as complements.
Exam
There will be an oral exam at the end of the semester. Further details will be forthcoming.
Important links
News
Corona: Measures at the Center for Mathematics
24.6.22: Colloquium on occasion of the retirement of Herrn Prof. Dr. Carl-Friedrich Bödigheimer
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Prof. Dr. Jessica Fintzen new at the Mathematical Institute
Otto Toeplitz memorial fund established
Hausdorff Memorial Prize 2020/2021 awarded
Bachelorpreis 2020/21 der BMG verliehen
Prof. Christoph Thiele is holding the Clay Lecture 2022
Hausdorff Edition „Felix Hausdorff - Gesammelte Werke“
Prof. Catharina Stroppel invited as plenary speaker to the ICM 2022 in St. Petersburg
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Georg Oberdieck erhält Heinz Maier-Leibnitz-Preise 2020
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant