Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

Jason Murphy; Fabio Pusateri

doi:10.3934/dcds.2017089

Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

Jason Murphy, Fabio Pusateri

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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(C_ϵ^-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

Original language	English (US)
Pages (from-to)	2077-2102
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	37
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2017089
State	Published - Apr 2017

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Keywords

Almost global existence
Cubic NLS
Method of space-time resonances

Access to Document

10.3934/dcds.2017089

Cite this

@article{ac17abb7498242f882fe50deb8f36598,

title = "Almost global existence for cubic nonlinear Schr{\"o}dinger equations in one space dimension",

abstract = "We consider non-gauge-invariant cubic nonlinear Schr{\"o}dinger 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.",

keywords = "Almost global existence, Cubic NLS, Method of space-time resonances",

author = "Jason Murphy and Fabio Pusateri",

note = "Funding Information: 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.",

year = "2017",

month = apr,

doi = "10.3934/dcds.2017089",

language = "English (US)",

volume = "37",

pages = "2077--2102",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "4",

}

TY - JOUR

T1 - Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

AU - Murphy, Jason

AU - Pusateri, Fabio

N1 - Funding Information: 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.

PY - 2017/4

Y1 - 2017/4

N2 - 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.

AB - 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.

KW - Almost global existence

KW - Cubic NLS

KW - Method of space-time resonances

UR - http://www.scopus.com/inward/record.url?scp=85009167978&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009167978&partnerID=8YFLogxK

U2 - 10.3934/dcds.2017089

DO - 10.3934/dcds.2017089

M3 - Article

AN - SCOPUS:85009167978

SN - 1078-0947

VL - 37

SP - 2077

EP - 2102

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this