In this talk some results on the long-time behavior of dispersive equations with potentials will be presented. We will focus on the NLS equation in 3D with quadratic nonlinearity and small time dependent potential. The case of small time-independent magnetic potential will also be mentioned.These equations are of interest since they can be seen as models for the linearization of dispersive equations around special solutions. The method described consists in bringing together the space-time resonance theory of Germain, Masmoudi and Shatah with tools used in the study of the linear Schrodinger equation.

Zoom link: https://princeton.zoom.us/j/92147928280

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