Title

Almost Global Existence for Cubic Nonlinear Schrödinger Equations in One Space Dimension

Abstract

We consider non-gauge-invariant cubic nonlinear Schrödinger equations in one space dimension. We show that initial data of size ε in a weighted Sobolev space lead to solutions with sharp Lx decay up to time exp(-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

Department(s)

Mathematics and Statistics

Comments

J. M. was supported by the NSF Postdoctoral Fellowship DMS-1400706. F. P. was supported in part by NSF grant DMS-1265875. We thank the anonymous referee for their comments and suggestions.

Keywords and Phrases

Almost global existence; Cubic NLS; Method of space-time resonances

International Standard Serial Number (ISSN)

1078-0947; 1553-5231

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Apr 2017

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