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Well-posedness for the fifth-order shallow water equations
Jia, Yueling2; Huo, Zhaohui1,3
2009-03-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume246Issue:6Pages:2448-2467
AbstractThe 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.
KeywordFifth-order shallow water equations Fourier restriction norm Bilinear estimates Trilinear estimates Local well-posedness
DOI10.1016/j.jde.2008.10.027
Language英语
Funding ProjectNSF of China[10701013] ; NSF of China[10601006]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000264013600012
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/7088
Collection数学所
Corresponding AuthorHuo, Zhaohui
Affiliation1.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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