Nonlinear Schroedinger equation with a Magnetic Potential

PDE Seminar
Tuesday, October 5, 2010 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 255
Prof. Shijun Zheng – Georgia Southern University – szheng@georgiasouthern.edu
Ronghua Pan
The dissipative mechanism of Schroedinger equation is mathematically described by the decay estimate of solutions. In this talk I mainly focused on the use of harmonic analysis techniques to obtain suitable time decay estimates and then prove the local wellposedness for semilinear Schroedinger equation in certain external magnetic field. It turns out that the scattering with a potential may lead to understanding of the wellposedness of NLS in the presence of nonsmooth or large initial data. Part of this talk is a joint work with Zhenqiu Zhang.