Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$

J. Colliander, Justin Holmer, Monica Vişan, Xiaoyi Zhang

Type: Article

Publication Date: 2008-01-01

Citations: 28

DOI: https://doi.org/10.3934/cpaa.2008.7.467

Abstract

We consider the Cauchy problem for a family of semilinear defocusing Schrödinger 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 <em>a priori</em> $L_{t,x}^8$ spacetime control on solutions.

Locations

Communications on Pure &amp Applied Analysis - View - PDF
arXiv (Cornell University) - View - PDF

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