# ALMOST GLOBAL EXISTENCE FOR CUBIC NONLINEAR SCHRODINGER EQUATIONS IN ONE SPACE DIMENSION

## Author(s): Murphy, Jason; Pusateri, Fabio Giuseppe

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 Abstract: We consider non-gauge-invariant cubic nonlinear Schrodinger equations in one space dimension. We show that initial data of size epsilon in a weighted Sobolev space lead to solutions with sharp L-x(infinity) decay up to time exp(C-epsilon(-2)). We also exhibit norm growth beyond this time for a specific choice of nonlinearity. Publication Date: Apr-2017 Electronic Publication Date: Apr-2017 Citation: Murphy, Jason, Pusateri, Fabio. (2017). ALMOST GLOBAL EXISTENCE FOR CUBIC NONLINEAR SCHRODINGER EQUATIONS IN ONE SPACE DIMENSION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 37 (2077 - 2102. doi:10.3934/dcds.2017089 DOI: doi:10.3934/dcds.2017089 ISSN: 1078-0947 EISSN: 1553-5231 Pages: 2077 - 2102 Type of Material: Journal Article Journal/Proceeding Title: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS Version: Author's manuscript