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

James Colliander; Justin Holmer; Monica Visan; Xiaoyi Zhang

doi:10.3934/cpaa.2008.7.467

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

Journal article

Open access

Peer reviewed

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

James Colliander, Justin Holmer, Monica Visan and Xiaoyi Zhang

Communications on pure and applied analysis, Vol.7(3), pp.467-489

05/01/2008

DOI: 10.3934/cpaa.2008.7.467

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Abstract

We consider the Cauchy problem for a family of semilinear defocusing Schrodinger 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.

Mathematics

Physical Sciences

Mathematics, Applied

Science & Technology

Details

Title: Subtitle: Global existence and scattering for rough solutions to generalized nonlinear Schrodinger equations on R
Creators: James Colliander - Univ Toronto, Toronto, ON, Canada
Justin Holmer - Univ Calif Berkeley, Berkeley, CA 94720 USA
Monica Visan
Xiaoyi Zhang - Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100864, Peoples R China
Resource Type: Journal article
Publication Details: Communications on pure and applied analysis, Vol.7(3), pp.467-489
Publisher: AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/cpaa.2008.7.467
ISSN: 1534-0392
eISSN: 1553-5258
Number of pages: 23
Language: English
Date published: 05/01/2008
Academic Unit: Mathematics
Record Identifier: 9984241049802771

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