May  2008, 7(3): 467-489. doi: 10.3934/cpaa.2008.7.467

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

1. 

University of Toronto, Toronto, Ontario, M5S 2E4

2. 

Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720

3. 

Institute for Advanced Study and M.S.R.I., United States

4. 

Academy of Mathematics and System Sciences, Chinese Academy of Sciences and M.S.R.I., China

Received  May 2007 Revised  October 2007 Published  February 2008

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 a priori $L_{t,x}^8$ spacetime control on solutions.
Citation: J. Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure & Applied Analysis, 2008, 7 (3) : 467-489. doi: 10.3934/cpaa.2008.7.467
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