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

School of Mathematics and Statistics

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

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2619-2630
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	151
Issue number	6
DOIs	https://doi.org/10.1090/proc/16325
Publication status	Published - 1 Jun 2023

Keywords

Fourth-order Schrödinger equation
dispersive estimate
long time behavior

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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. 2473–2517]. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.",

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AU - Zhao, Zehua

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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.

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KW - dispersive estimate

KW - long time behavior

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

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