Well-posedness for the fifth-order shallow water equations | |
Jia, Yueling2; Huo, Zhaohui1,3 | |
2009-03-15 | |
Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS |
ISSN | 0022-0396 |
Volume | 246Issue:6Pages:2448-2467 |
Abstract | The Cauchy problems for some kind of fifth-order shallow water equations partial derivative(t)u + alpha partial derivative(5)(x)u + beta partial derivative(3)(x)u + gamma partial derivative(u)(x) + F(u, partial derivative(x)u, partial derivative(2)(x)u) = 0, x, t is an element of R x R, are considered by the Fourier restriction norm method, where nonlinear terms F(u, partial derivative(x)u, partial derivative(2)(x)u) are mu partial derivative(x)(u(k)), k = 2,3, mu u partial derivative(2)(x)u or mu partial derivative(x)u partial derivative(2)(x)u respectively. The local well-posedness is established for data in H(s)(R) with s > -7/4 for the Kawahara equation (F = mu partial derivative(x)(u(2))) and is established for data in H(s)(R) with s >= -1/4 for the modified Kawahara equation (F = mu partial derivative(x)(u(3))), respectively. Moreover, the local result is established for data in H(s)(R) with s > 0 if F = mu u partial derivative(2)(x)u and is established for data in HI(R) with s > -1/4 if F = mu partial derivative(x)u partial derivative(2)(x) u, respectively. (C) 2008 Elsevier Inc. All rights reserved. |
Keyword | Fifth-order shallow water equations Fourier restriction norm Bilinear estimates Trilinear estimates Local well-posedness |
DOI | 10.1016/j.jde.2008.10.027 |
Language | 英语 |
Funding Project | NSF of China[10701013] ; NSF of China[10601006] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000264013600012 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/7088 |
Collection | 数学所 |
Corresponding Author | Huo, Zhaohui |
Affiliation | 1.Chinese Acad Sci, Inst Math Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China 3.City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China |
Recommended Citation GB/T 7714 | Jia, Yueling,Huo, Zhaohui. Well-posedness for the fifth-order shallow water equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2009,246(6):2448-2467. |
APA | Jia, Yueling,&Huo, Zhaohui.(2009).Well-posedness for the fifth-order shallow water equations.JOURNAL OF DIFFERENTIAL EQUATIONS,246(6),2448-2467. |
MLA | Jia, Yueling,et al."Well-posedness for the fifth-order shallow water equations".JOURNAL OF DIFFERENTIAL EQUATIONS 246.6(2009):2448-2467. |
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