Diff. Geom, Math. Phys., PDE: Zaher Hani
Topic
Scattering for nonlinear dispersive equations in the presence of a potential
Speakers
Details
Questions related to the asymptotic behavior of nonlinear dispersive equations in the presence of a potential term are of great interest both for mathematical and physical reasons. Our main concern will be equations with low-degree nonlinearities, namely below the Strauss exponent threshold, for which classical energy and decay methods fail to suffice. For this, we we use the spectral theory of the operator H=-\Delta+V to develop a space-time resonance analysis adapted to the inhomogeneous setting. A key ingredient in this setup is the development of a sufficiently comprehensive multilinear harmonic analysis in the context of the corresponding distorted Fourier transform. This turns out to exhibit several intriguing differences in comparison to the unperturbed Euclidean setting (no matter how small V is). As a first application, we treat the case of a quadratic nonlinear Schrodinger equation on \R^3.
This is joint work with Pierre Germain and Samuel Walsh (Courant Institute, NYU).
This is joint work with Pierre Germain and Samuel Walsh (Courant Institute, NYU).
Additional Information
Location: ESB 4127
Zaher Hani, New York University
Zaher Hani, New York University
This is a Past Event
Event Type
Scientific, Seminar
Date
March 18, 2013
Time
-
Location