Global existence of small classical solutions to nonlinear Schrödinger equations

Tohru Ozawa; Jian Zhai

doi:10.1016/j.anihpc.2006.11.010

Global existence of small classical solutions to nonlinear Schrödinger equations

Tohru Ozawa, Jian Zhai

研究成果: Article › 査読

18 被引用数 (Scopus)

抄録

We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.

本文言語	English
ページ（範囲）	303-311
ページ数	9
ジャーナル	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
巻	25
号	2
DOI	https://doi.org/10.1016/j.anihpc.2006.11.010
出版ステータス	Published - 2008
外部発表	はい

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

文献へのアクセス

10.1016/j.anihpc.2006.11.010

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引用スタイル

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title = "Global existence of small classical solutions to nonlinear Schr{\"o}dinger equations",

abstract = "We study the global Cauchy problem for nonlinear Schr{\"o}dinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.",

keywords = "Nonlinear Schr{\"o}dinger equations, Schr{\"o}dinger maps",

author = "Tohru Ozawa and Jian Zhai",

note = "Funding Information: This work started when T.O. visited Zhejiang University in 2004 and took a preliminary shape when J.Z. visited Hokkaido University in 2005. Part of this work was done while T.O. visited Courant Institute in 2005. T.O. would like to thank Professor Jalal Shatah for his hospitality and enlightning discussions. J.Z. is partly supported by NSFC 10571157.",

year = "2008",

doi = "10.1016/j.anihpc.2006.11.010",

language = "English",

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AU - Ozawa, Tohru

AU - Zhai, Jian

N1 - Funding Information: This work started when T.O. visited Zhejiang University in 2004 and took a preliminary shape when J.Z. visited Hokkaido University in 2005. Part of this work was done while T.O. visited Courant Institute in 2005. T.O. would like to thank Professor Jalal Shatah for his hospitality and enlightning discussions. J.Z. is partly supported by NSFC 10571157.

PY - 2008

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N2 - We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.

AB - We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.

KW - Nonlinear Schrödinger equations

KW - Schrödinger maps

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JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

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