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

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1389-1405
Number of pages	17
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2013.33.1389
Publication status	Published - 2013 Apr

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Keywords

Angular regularity
Critical nonlinearity below L
Global well-posedness
Hartree equations
Weighted Strichartz estimate

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics
Analysis

Cite this

Cho, Y., Hwang, G., & Ozawa, T. (2013). Global well-posedness of critical nonlinear Schrödinger equations below L² Discrete and Continuous Dynamical Systems- Series A, 33(4), 1389-1405. https://doi.org/10.3934/dcds.2013.33.1389

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AU - Ozawa, Tohru

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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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Access to Document

10.3934/dcds.2013.33.1389