Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces

Nakao Hayashi; Pavel I. Naumkin

Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces

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

Abstract

We consider the Cauchy problem for the cubic nonlinear Schrödinger equation {equation presented} The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u₀ ∈ H^α∩H^0,α with α > 1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u₀ ∈ H²∩H^0,2. Also we find the large-time asymptotics of solutions.

Original language	English
Pages (from-to)	801-828
Number of pages	28
Journal	Differential and Integral Equations
Volume	24
Issue number	9-10
Publication status	Published - 2011 Sept
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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title = "Global existence for the cubic nonlinear Schr{\"o}dinger equation in lower order Sobolev spaces",

abstract = "We consider the Cauchy problem for the cubic nonlinear Schr{\"o}dinger equation {equation presented} The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u0 ∈ Hα∩H0,α with α > 1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u0 ∈ H2∩H0,2. Also we find the large-time asymptotics of solutions.",

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

year = "2011",

month = sep,

language = "English",

volume = "24",

pages = "801--828",

journal = "Differential and Integral Equations",

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AU - Naumkin, Pavel I.

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N2 - We consider the Cauchy problem for the cubic nonlinear Schrödinger equation {equation presented} The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u0 ∈ Hα∩H0,α with α > 1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u0 ∈ H2∩H0,2. Also we find the large-time asymptotics of solutions.

AB - We consider the Cauchy problem for the cubic nonlinear Schrödinger equation {equation presented} The aim of the present paper is to consider problem (0.1) in low-order Sobolev spaces, when the initial data u0 ∈ Hα∩H0,α with α > 1/2. In our previous paper [7] we proved the global existence of solutions to (0.1) if the initial data u0 ∈ H2∩H0,2. Also we find the large-time asymptotics of solutions.

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JF - Differential and Integral Equations

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ER -

Global existence for the cubic nonlinear Schrödinger equation in lower order Sobolev spaces

Abstract

ASJC Scopus subject areas

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