Existence and scattering of small solutions to a Boussinesq type equation of sixth order

Suxia Xia; Jia Yuan

doi:10.1016/j.na.2010.04.028

Existence and scattering of small solutions to a Boussinesq type equation of sixth order

Suxia Xia^*
, Jia Yuan

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

18 引用（Scopus）

摘要

In this paper, we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term f(u) behaving as u^p(p>1) as u→0 in ℝⁿ,n≥1. The main method and techniques used in our paper are the LittlewoodPaley dyadic decomposition, the stationary phase estimate and some properties of Bessel function.

源语言	英语
页（从-至）	1015-1027
页数	13
期刊	Nonlinear Analysis, Theory, Methods and Applications
卷	73
期	4
DOI	https://doi.org/10.1016/j.na.2010.04.028
出版状态	已出版 - 15 8月 2010

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abstract = "In this paper, we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term f(u) behaving as up(p>1) as u→0 in ℝn,n≥1. The main method and techniques used in our paper are the LittlewoodPaley dyadic decomposition, the stationary phase estimate and some properties of Bessel function.",

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author = "Suxia Xia and Jia Yuan",

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AU - Xia, Suxia

AU - Yuan, Jia

PY - 2010/8/15

Y1 - 2010/8/15

N2 - In this paper, we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term f(u) behaving as up(p>1) as u→0 in ℝn,n≥1. The main method and techniques used in our paper are the LittlewoodPaley dyadic decomposition, the stationary phase estimate and some properties of Bessel function.

AB - In this paper, we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term f(u) behaving as up(p>1) as u→0 in ℝn,n≥1. The main method and techniques used in our paper are the LittlewoodPaley dyadic decomposition, the stationary phase estimate and some properties of Bessel function.

KW - Boussinesq type equation

KW - Cauchy problem

KW - Dispersive estimate

KW - Scattering

UR - https://www.scopus.com/pages/publications/77955325672

U2 - 10.1016/j.na.2010.04.028

DO - 10.1016/j.na.2010.04.028

M3 - 文章

AN - SCOPUS:77955325672

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VL - 73

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 4

ER -

Existence and scattering of small solutions to a Boussinesq type equation of sixth order

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