ON THE DECAY PROPERTY OF THE CUBIC FOURTH-ORDER SCHRÖDINGER EQUATION

Xueying Yu; Haitian Yue; Zehua Zhao

doi:10.1090/proc/16325

ON THE DECAY PROPERTY OF THE CUBIC FOURTH-ORDER SCHRÖDINGER EQUATION

Xueying Yu
, Haitian Yue
, Zehua Zhao

University of Washington
ShanghaiTech University
Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

3 引用（Scopus）

摘要

In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on R^d (5 ≤ d ≤ 8) enjoys the same decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result by Pausader [J. Funct. Anal. 256 (2009), pp. 2473–2517]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.

源语言	英语
页（从-至）	2619-2630
页数	12
期刊	Proceedings of the American Mathematical Society
卷	151
期	6
DOI	https://doi.org/10.1090/proc/16325
出版状态	已出版 - 1 6月 2023
已对外发布	是

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title = "ON THE DECAY PROPERTY OF THE CUBIC FOURTH-ORDER SCHR{\"O}DINGER EQUATION",

abstract = "In this short paper, we prove that the solution of the cubic fourth-order Schr{\"o}dinger equation (4NLS) on Rd (5 ≤ d ≤ 8) enjoys the same decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result by Pausader [J. Funct. Anal. 256 (2009), pp. 2473{\textendash}2517]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.",

keywords = "Fourth-order Schr{\"o}dinger equation, dispersive estimate, long time behavior",

author = "Xueying Yu and Haitian Yue and Zehua Zhao",

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AU - Yu, Xueying

AU - Yue, Haitian

AU - Zhao, Zehua

PY - 2023/6/1

Y1 - 2023/6/1

N2 - In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on Rd (5 ≤ d ≤ 8) enjoys the same decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result by Pausader [J. Funct. Anal. 256 (2009), pp. 2473–2517]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.

AB - In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on Rd (5 ≤ d ≤ 8) enjoys the same decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result by Pausader [J. Funct. Anal. 256 (2009), pp. 2473–2517]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.

KW - Fourth-order Schrödinger equation

KW - dispersive estimate

KW - long time behavior

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JF - Proceedings of the American Mathematical Society

IS - 6

ER -

ON THE DECAY PROPERTY OF THE CUBIC FOURTH-ORDER SCHRÖDINGER EQUATION

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