Analysis & Applied Math

Event Information Quadratic NLS with potentials
14:10 on Friday November 15, 2019
15:00 on Friday November 15, 2019
BA6183, Bahen Center, 40 St. George St.
Tristan Leger

New York University, Courant Institute

In this talk some recent results on the long-time behavior of dispersive equations with potentials will be presented. More precisely, we will focus on the NLS equation in 3D with quadratic nonlinearity and two types of potentials (electric time dependent on one hand, and electromagnetic time independent on the other). These equations are of interest since they constitute good models for the linearization of dispersive equations around special solutions. The methods described consist in bringing together the space-time resonance theory of Germain, Masmoudi and Shatah with tools used in the study of the linear Schroedinger equation (Strichartz and smoothing estimates, boundedness and representation of wave operators).