Björn Walther: Long Time Behaviour for the (Fractional) Schrödinger Equation with Time-dependent Potential.
Tid: On 2013-12-18 kl 13.15
Plats: Seminarierum 3721, Lindstedt
Abstract. In a paper from 2003 (Lecture Notes in Mathematics 1807) Bourgain proves a priori estimates for solutions to the time-dependent Schr\"odinger equation with small time-dependent complex-valued potentials fulfilling certain support conditions. In our work under progress we attempt to extend these results to the fractional Schr\"odinger equation. We also try to weaken the support conditions. Implicit in Bourgain's proof is an inequality expressing the well-known gain of regularity by 1/2 derivatives. We study the corresponding phenomenon for the fractional Schr\"odinger equation.