Global existence and scattering for rough solutions to generalized nonlinear Schr\"odinger equations on $\R$

J. Colliander; J. Holmer; M. Visan; X. Zhang

arxiv: math/0612452 · v1 · submitted 2006-12-15 · 🧮 math.AP

Global existence and scattering for rough solutions to generalized nonlinear Schr\"odinger equations on R

J. Colliander , J. Holmer , M. Visan , X. Zhang This is my paper

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keywords equationsglobalodingerscatteringschrsolutionsanalysiscauchy

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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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Global existence and scattering for rough solutions to generalized nonlinear Schr\"odinger equations on R

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