Resonances and null structures in weakly dispersive equations

Fabio Pusateri, New York University
Fine Hall 314

We show a result about global existence of small solutions for a class of scattering critical nonlinear dispersive equations. The problem we consider originates from a classical result of S. Klainerman on the wave equation. Our proof is based on the method of space-time resonances, recently introduced by Germain, Masmoudi and Shatah. In particular, we focus on the relation between resonances and null structures. We will also discuss some related application to scattering critical equations of Schrodinger type.