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Hyperbolic & Dispersive PDE Seminar

Gavin Stewart -- Scattering and localized states for nonlinear Schrödinger equations

Gavin Stewart - Rutgers University

Location:  Hill 705
Date & time: Thursday, 07 December 2023 at 2:30PM - 3:30PM

In this talk, I will discuss some results on the long time behavior of nonlinear Schrödinger equations with potentials.  First, I will show that solutions which are initially localized and nonradiative can only spread slowly in space.  Then, I will focus on the mass supercritical equation, and show that solutions decompose into a free wave and a slowly spreading remainder.  A key ingredient in these arguments is the use of Morawetz and interaction Morawetz estimates localized to an exterior region in space-time.  This is joint work with Avy Soffer.