V5B4 Selected Topics in PDE and Mathematical Models - Dispersive Equations
Wintersemester 2017/2018
Instructor: Dr. Xian Liao
Lectures:
Topics: We will focus on the mathematical theory of nonlinear Schrödinger equations (NLS)
- Well-posedness issue of (NLS)
- - Local & Global well-posedness in L2 / H1, by use of Strichartz estimates & Sobolev embedding & conservation laws
- Long time behaviour of the solutions of (NLS)
- - Blowup & Scattering, by use of Virial & Morawetz idenities
- Solitary waves of (NLS)
- - Orbital stability, by use of variational description & concentration-compactness
- Conserved energies for one dimensional cubic (NLS)
- - Conserved energies, by use of invariant transmission coefficient
Prerequisites:
References:
- T. Cazenave: Semilinear Schrödinger equations.
- F. Linares, G. Ponce: Introduction to nonlinear dispersive equations.
- T. Tao: Nonlinear dispersive equations - local and global analysis.
- J. Colliander, M. Keel, G. Staffilani, H. Takaoka, T.Tao: The theory of nonlinear Schödinger equations.
- H. Koch, D. Tataru: Conserved energies for the cubic NLS in 1-d.
Oral Exams: 31.01.2018 & 21.03.2018
News
The Mathematical Institute mourns Günter Harder
Floris van Doorn and coauthors receive the Skolem Award
Hausdorff Center for Mathematics receives 7 additional years of funding
Markus Hausmann receives Minkwoski medal of the DMV
Rajula Srivastava receives Maryam Mirzakhani New Frontiers Prize
Dennis Gaitsgory receives Breakthrough Prize in Mathematics 2025
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