Global existence and scattering for rough solutions to generalized nonlinear Schr\" odinger equations on $\R$
arXiv preprint math/0612452, 2006•arxiv.org
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} $ L^ 8_ {t, x} $ spacetime control on solutions.
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} $ L^ 8_ {t, x} $ spacetime control on solutions.
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.
arxiv.org
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