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 L∞x decay up to time exp(Cε-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.
Recommended Citation
J. Murphy and F. Pusateri, "Almost Global Existence for Cubic Nonlinear Schrödinger Equations in One Space Dimension," Discrete and Continuous Dynamical Systems- Series A, vol. 37, no. 4, pp. 2077 - 2102, American Institute of Mathematical Sciences (AIMS), Apr 2017.
The definitive version is available at https://doi.org/10.3934/dcds.2017089
Department(s)
Mathematics and Statistics
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
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.