Critical nonlinear Schrödinger equations in higher space dimensions

Nakao Hayashi; Chunhua Li; Pavel I. Naumkin

doi:10.2969/jmsj/77127712

Critical nonlinear Schrödinger equations in higher space dimensions

Nakao Hayashi, Chunhua Li, Pavel I. Naumkin

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

1 Citation (Scopus)

Abstract

We study the critical nonlinear Schrödinger equations iδ_tu +1/2Δu = λ|u|^2/nu; (t; x) ∈ R⁺ × Rⁿ; in space dimensions n ≥ 4; where λ ∈ R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.

Original language	English
Pages (from-to)	1475-1492
Number of pages	18
Journal	Journal of the Mathematical Society of Japan
Volume	70
Issue number	4
DOIs	https://doi.org/10.2969/jmsj/77127712
Publication status	Published - 2018
Externally published	Yes

Keywords

Critical NLS equations
Higher space dimensions
Large time asymptotics

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/77127712

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@article{082aa9ef9cd0416497dafea957974279,

title = "Critical nonlinear Schr{\"o}dinger equations in higher space dimensions",

abstract = "We study the critical nonlinear Schr{\"o}dinger equations iδtu +1/2Δu = λ|u|2/nu; (t; x) ∈ R+ × Rn; in space dimensions n ≥ 4; where λ ∈ R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.",

keywords = "Critical NLS equations, Higher space dimensions, Large time asymptotics",

author = "Nakao Hayashi and Chunhua Li and Naumkin, {Pavel I.}",

note = "Funding Information: The firtst author was partially supported by JSPS KAKENHI Grant Numbers JP25220702, JP15H03630. The second author was partially supported by NNSFC Grant No.11461074. The third author was partially supported by CONACYT and PAPIIT project IN100616. Publisher Copyright: {\textcopyright} 2018 The Mathematical Society of Japan.",

year = "2018",

doi = "10.2969/jmsj/77127712",

language = "English",

volume = "70",

pages = "1475--1492",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

number = "4",

}

TY - JOUR

T1 - Critical nonlinear Schrödinger equations in higher space dimensions

AU - Hayashi, Nakao

AU - Li, Chunhua

AU - Naumkin, Pavel I.

N1 - Funding Information: The firtst author was partially supported by JSPS KAKENHI Grant Numbers JP25220702, JP15H03630. The second author was partially supported by NNSFC Grant No.11461074. The third author was partially supported by CONACYT and PAPIIT project IN100616. Publisher Copyright: © 2018 The Mathematical Society of Japan.

PY - 2018

Y1 - 2018

N2 - We study the critical nonlinear Schrödinger equations iδtu +1/2Δu = λ|u|2/nu; (t; x) ∈ R+ × Rn; in space dimensions n ≥ 4; where λ ∈ R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.

AB - We study the critical nonlinear Schrödinger equations iδtu +1/2Δu = λ|u|2/nu; (t; x) ∈ R+ × Rn; in space dimensions n ≥ 4; where λ ∈ R. We prove the global in time existence of solutions to the Cauchy problem under the assumption that the absolute value of Fourier transform of the initial data is bounded below by a positive constant. Also we prove the two side sharp time decay estimates of solutions in the uniform norm.

KW - Critical NLS equations

KW - Higher space dimensions

KW - Large time asymptotics

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U2 - 10.2969/jmsj/77127712

DO - 10.2969/jmsj/77127712

M3 - Article

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VL - 70

SP - 1475

EP - 1492

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -

Critical nonlinear Schrödinger equations in higher space dimensions

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Keywords

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