RG Analysis and Partial Differential Equations
S4B1 - Graduate Seminar on Analysis (Summer term 2015)
Dozenten:
Termin:
Topic: Blow-up for dispersive equations
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In this seminar we will study blow-up solutions to various dispersive
equations. It is a striking feature of critical and supercritical
equations (the terms will be explained in the seminar) that there are
solutions which blow-up in finite time. Blow-up of an analytic
solution is related to a break down of the mathematical model.
We will be interested in sufficient criteria on initial data for blow-up,
as well as in a precise
description of the blow-up.
Literature:
- Sulem and Sulem: The nonlinear Schroedinger equation, Springer
- Shatah and Struwe: Geometric wave equations
- Tao: Nonlinear dispersive equations
- Sogge: Lectures on non-linear wave equations
- Lecture notes by Sigmund Selberg
- Notes by Andrew Lawrie
Prerequests:
Schedule
- April 20: Roland Donninger: Wellposedness for nonlinear wave equations
- April 27: Tillman Ritschl: Mechanisms of blow-up
- May 4: Amos Schickowski: Existence and stability of solitons and concentration compactness I
- May 11: Immanuel Zachhuber: Existence and stability of solitons and concentration compactness II
- May 18: Tobias Schmidt: Harmonic map heat flow
- May 25: public holiday
- June 1: Zipeng Rao: The Ljapunov functional of Antonini and Merle
- June 8: Wenhui Shi: Uniform blow rates
- June 15: Adina Chirila: The heuristics of blow up for NLS (Sulem and Sulem)
- June 22: Emil Wiedemann: Blowup for supercritical gKdV
- June 29: Gennardy Uralcev: Critical blow-up I
- July 6: Lisa Onkes: Critical blow-up II
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