Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

T. Ozawa; K. Yamauchi

doi:10.1016/j.jmaa.2009.09.033

Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

T. Ozawa^*, K. Yamauchi

^*Corresponding author for this work

School of Advanced Science and Engineering

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

18 Citations (Scopus)

Abstract

We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.

Original language	English
Pages (from-to)	492-497
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	364
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.09.033
Publication status	Published - 2010 Apr 15

Keywords

Analytic smoothing effect
Global solutions
Nonlinear Schrödinger equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2009.09.033

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title = "Analytic smoothing effect for global solutions to nonlinear Schr{\"o}dinger equations",

abstract = "We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schr{\"o}dinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.",

keywords = "Analytic smoothing effect, Global solutions, Nonlinear Schr{\"o}dinger equations",

author = "T. Ozawa and K. Yamauchi",

year = "2010",

month = apr,

day = "15",

doi = "10.1016/j.jmaa.2009.09.033",

language = "English",

volume = "364",

pages = "492--497",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

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T1 - Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

AU - Ozawa, T.

AU - Yamauchi, K.

PY - 2010/4/15

Y1 - 2010/4/15

N2 - We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.

AB - We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrödinger equation in space dimension n ≥ 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data.

KW - Analytic smoothing effect

KW - Global solutions

KW - Nonlinear Schrödinger equations

UR - http://www.scopus.com/inward/record.url?scp=72149128906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72149128906&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2009.09.033

DO - 10.1016/j.jmaa.2009.09.033

M3 - Article

AN - SCOPUS:72149128906

SN - 0022-247X

VL - 364

SP - 492

EP - 497

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Analytic smoothing effect for global solutions to nonlinear Schrödinger equations

Abstract

Keywords

ASJC Scopus subject areas

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