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

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

2006-12-15

arxiv.org/abs/math/0612452v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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