Björn Walther: Long Time Behaviour for the (Fractional) Schrödinger Equation with Time-dependent Potential.

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.