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

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Scopus citations

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
State	Published - 2013.04

Keywords

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

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.3934/dcds.2013.33.1389

Cite this

@article{93e880729963491ea1be29b4cda8ebfb,

title = "Global well-posedness of critical nonlinear Schr{\"o}dinger equations below L2",

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",

year = "2013",

month = apr,

doi = "10.3934/dcds.2013.33.1389",

language = "English",

volume = "33",

pages = "1389--1405",

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

issn = "1078-0947",

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TY - JOUR

T1 - Global well-posedness of critical nonlinear Schrödinger equations below L2

AU - Cho, Yonggeun

AU - Hwang, Gyeongha

AU - Ozawa, Tohru

PY - 2013/4

Y1 - 2013/4

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.

KW - Angular regularity

KW - Critical nonlinearity below L

KW - Global well-posedness

KW - Hartree equations

KW - Weighted Strichartz estimate

UR - https://www.scopus.com/pages/publications/84872111706

U2 - 10.3934/dcds.2013.33.1389

DO - 10.3934/dcds.2013.33.1389

M3 - Journal article

AN - SCOPUS:84872111706

SN - 1078-0947

VL - 33

SP - 1389

EP - 1405

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -