On the global well-posedness for the nonlinear Schrdinger equations with large initial data of infinite L2 norm

Ryosuke Hyakuna; Takamasa Tanaka; Masayoshi Tsutsumi

doi:10.1016/j.na.2010.10.003

On the global well-posedness for the nonlinear Schrdinger equations with large initial data of infinite L2 norm

Ryosuke Hyakuna^*, Takamasa Tanaka, Masayoshi Tsutsumi

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

It is shown that the Cauchy problem for the nonlinear Schrdinger equations iu_t+△u±|u|^p-1u=0,x∈ℝ^d, t>0 is globally well-posed for a class of initial data which lie in a Lq space with q near 2 when 1<p<1+4d and d≤4.

Original language	English
Pages (from-to)	1304-1319
Number of pages	16
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	74
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2010.10.003
Publication status	Published - 2011 Feb 15

Keywords

Cauchy problem
Global solution
Large initial data
Lp-initial data
Nonlinear Schrdinger equations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2010.10.003

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abstract = "It is shown that the Cauchy problem for the nonlinear Schrdinger equations iut+△u±|u|p-1u=0,x∈ℝd, t>0 is globally well-posed for a class of initial data which lie in a Lq space with q near 2 when 1",

keywords = "Cauchy problem, Global solution, Large initial data, Lp-initial data, Nonlinear Schrdinger equations",

author = "Ryosuke Hyakuna and Takamasa Tanaka and Masayoshi Tsutsumi",

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doi = "10.1016/j.na.2010.10.003",

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T1 - On the global well-posedness for the nonlinear Schrdinger equations with large initial data of infinite L2 norm

AU - Hyakuna, Ryosuke

AU - Tanaka, Takamasa

AU - Tsutsumi, Masayoshi

PY - 2011/2/15

Y1 - 2011/2/15

N2 - It is shown that the Cauchy problem for the nonlinear Schrdinger equations iut+△u±|u|p-1u=0,x∈ℝd, t>0 is globally well-posed for a class of initial data which lie in a Lq space with q near 2 when 1

AB - It is shown that the Cauchy problem for the nonlinear Schrdinger equations iut+△u±|u|p-1u=0,x∈ℝd, t>0 is globally well-posed for a class of initial data which lie in a Lq space with q near 2 when 1

KW - Cauchy problem

KW - Global solution

KW - Large initial data

KW - Lp-initial data

KW - Nonlinear Schrdinger equations

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DO - 10.1016/j.na.2010.10.003

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EP - 1319

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

On the global well-posedness for the nonlinear Schrdinger equations with large initial data of infinite L2 norm

Abstract

Keywords

ASJC Scopus subject areas

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