KMS Of Academy of mathematics and systems sciences, CAS
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, Boling3; Huo, Zhaohui1,2 | |
2020 | |
Source Publication | FORUM MATHEMATICUM |
ISSN | 0933-7741 |
Volume | 32Issue:1Pages:151-187 |
Abstract | 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. |
Keyword | Well-posedness higher-order intermediate long wave equation higher-order Benjamin-Ono equation modified energy |
DOI | 10.1515/forum-2019-0133 |
Indexed By | SCI |
Language | 英语 |
Funding Project | NSFC[11471323] ; NSFC[11571254] ; NSFC[11771444] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000505560100010 |
Publisher | WALTER DE GRUYTER GMBH |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50502 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Huo, Zhaohui |
Affiliation | 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 |
Recommended Citation 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. |
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