Analysis Seminar

The Asymptotic States of Nonlinear Schrödinger Type equations

Speaker: Any Soffer, Rutgers University

Location: Warren Weaver Hall 312

Date: Thursday, December 16, 2021, 11 a.m.


I will describe a new approach to scattering theory, which allows the analysis of interaction terms which are linear and time dependent, and nonlinear terms as well. This is based on deriving (exterior) propagation estimates for such equations, which micro-localize the asymptotic states as time goes to infinity.
In particular, the free part of the solution concentrates on the propagation set (x=vt), and the localized leftover is characterized in the phase-space as well.
The NLS with radial data in three dimensions is considered, and it is shown that besides the free asymptotic wave, in general, the localized part is smooth, and is localized in the region where |x|^2 is less than t.
Furthermore, the localized part has a massive core and possibly a halo which maybe a self-similar solution.
This work is joint with Baoping Liu