PDE/Analysis Seminar - "Global well-posedness in the derivative NLS equation", Jiaqi Liu
University of Toronto
Title: Global well-posedness in the derivative NLS equation
Abstract: We study the Derivative Nonlinear Schroedinger equation for generic initial conditions in weighted Sobolev spaces that can support finitely bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full description of the long- time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. We use the nonlinear steepest descent method of Deift and Zhou complemented by the recent work of Borghese-Jenkins-McLaughlin on soliton resolution for the focusing nonlinear Schroedinger equation.