Global existence and scattering for rough solutions to generalized nonlinear Schr\"odinger equations on $\R$
Analysis of PDEs
2007-05-23 v1
Abstract
We consider the Cauchy problem for a family of semilinear defocusing Schr\"odinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving \emph{a priori} spacetime control on solutions.
Keywords
Cite
@article{arxiv.math/0612452,
title = {Global existence and scattering for rough solutions to generalized nonlinear Schr\"odinger equations on $\R$},
author = {J. Colliander and J. Holmer and M. Visan and X. Zhang},
journal= {arXiv preprint arXiv:math/0612452},
year = {2007}
}