Global well-posedness of critical nonlinear Schrödinger equations below L2

Yonggeun Cho; Gyeongha Hwang; Tohru Ozawa

doi:10.3934/dcds.2013.33.1389

Global well-posedness of critical nonlinear Schrödinger equations below L²

Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

先進理工学部

研究成果: Article › 査読

8 被引用数 (Scopus)

抄録

The global well-posedness on the Cauchy problem of nonlinear Schrödinger equations (NLS) is studied for a class of critical nonlinearity below L² in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s _c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.

本文言語	English
ページ（範囲）	1389-1405
ページ数	17
ジャーナル	Discrete and Continuous Dynamical Systems- Series A
巻	33
号	4
DOI	https://doi.org/10.3934/dcds.2013.33.1389
出版ステータス	Published - 2013 4

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcds.2013.33.1389

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引用スタイル

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abstract = "The global well-posedness on the Cauchy problem of nonlinear Schr{\"o}dinger equations (NLS) is studied for a class of critical nonlinearity below L2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.",

keywords = "Angular regularity, Critical nonlinearity below L, Global well-posedness, Hartree equations, Weighted Strichartz estimate",

author = "Yonggeun Cho and Gyeongha Hwang and Tohru Ozawa",

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AU - Hwang, Gyeongha

AU - Ozawa, Tohru

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N2 - The global well-posedness on the Cauchy problem of nonlinear Schrödinger equations (NLS) is studied for a class of critical nonlinearity below L2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.

AB - The global well-posedness on the Cauchy problem of nonlinear Schrödinger equations (NLS) is studied for a class of critical nonlinearity below L2 in small data setting. We consider Hartree type (HNLS) and inhomogeneous power type NLS (PNLS). Since the critical Sobolev index s c is negative, it is rather difficult to analyze the nonlinear term. To overcome the difficulty we combine weighted Strichartz estimates in polar coordinates with new Duhamel estimates involving angular regularity.

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KW - Critical nonlinearity below L

KW - Global well-posedness

KW - Hartree equations

KW - Weighted Strichartz estimate

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