"Almost Global Existence for Cubic Nonlinear Schrödinger Equations in O" by Jason Murphy and Fabio Pusateri
 

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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