Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation

doi:10.1515/forum-2019-0133

CSpace

	Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation
	Guo, Boling 3; Huo, Zhaohui 1,2
	2020
发表期刊	FORUM MATHEMATICUM
ISSN	0933-7741
卷号	32 期号:1 页码:151-187
摘要	In this paper, the well-posedness of the higher-order Benjamin-Ono equation u(t) + H(u(xx ) + u(xxx )= uu(x) - partial derivative(x) (uH partial derivative(x)u + H (u partial derivative(x)u)) is considered. The modified energy method is introduced to consider the equation. It is shown that the Cauchy problem of the higher-order Benjamin-Ono equation is locally well-posed in H-3/4 without using the gauge transformation. Moreover, the well-posedness of the higher-order intermediate long wave equation u(t) + G(delta)(u(xx)) + u(xxx) = uu(x) - partial derivative(x)(uG(delta)partial derivative(x)u + G(delta)(u partial derivative(x)u)), G(delta) = F-x(-1) i(coth(delta xi))F-x, is considered. It is shown that the Cauchy problem of the higher-order intermediate long wave equation is locally well-posed in H-3/4.
关键词	Well-posedness higher-order intermediate long wave equation higher-order Benjamin-Ono equation modified energy
DOI	10.1515/forum-2019-0133
收录类别	SCI
语种	英语
资助项目	NSFC[11471323] ; NSFC[11571254] ; NSFC[11771444]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000505560100010
出版者	WALTER DE GRUYTER GMBH
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50502
专题	中国科学院数学与系统科学研究院
通讯作者	Huo, Zhaohui
作者单位	1.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Inst Appl Phys & Computat Math, POB 8009, Beijing 100088, Peoples R China
推荐引用方式 GB/T 7714	Guo, Boling,Huo, Zhaohui. Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation[J]. FORUM MATHEMATICUM,2020,32(1):151-187.
APA	Guo, Boling,&Huo, Zhaohui.(2020).Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation.FORUM MATHEMATICUM,32(1),151-187.
MLA	Guo, Boling,et al."Modified energy method and applications for the well-posedness for the higher-order Benjamin-Ono equation and the higher-order intermediate long wave equation".FORUM MATHEMATICUM 32.1(2020):151-187.