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
ERC Consolidator Grant for Dr. Evgeny Shinder
Jessica Fintzen wins Cole Prize
Vacancy: Office employee (Application deadline: 3.12.23)
Dr. Regula Krapf receives university teaching award
Prof. Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Prof. Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Prof. Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Rajula Srivastava receives Association for Women in Mathematics Dissertation Prize
Prof. Ana Caraiani wins a New Horizons in Mathematics Prizes 2023
Pius XI Medal awarded to Professor Peter Scholze
Prof. Valentin Blomer und Prof. Georg Oberdieck erhalten ERC grants
Grants for Mathematics students from Ukraine
Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant