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

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

18 Scopus citations

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 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.

Original language	English
Pages (from-to)	1015-1027
Number of pages	13
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	73
Issue number	4
DOIs	https://doi.org/10.1016/j.na.2010.04.028
State	Published - 15 Aug 2010

Keywords

Boussinesq type equation
Cauchy problem
Dispersive estimate
Scattering

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title = "Existence and scattering of small solutions to a Boussinesq type equation of sixth order",

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.",

keywords = "Boussinesq type equation, Cauchy problem, Dispersive estimate, Scattering",

author = "Suxia Xia and Jia Yuan",

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T1 - Existence and scattering of small solutions to a Boussinesq type equation of sixth order

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

SN - 0362-546X

VL - 73

SP - 1015

EP - 1027

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

Abstract

Keywords

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