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Well-posedness and inviscid limit behavior of solution for the generalized 1D Ginzburg-Landau equation
Huo, Zhaohui1,2; Jia, Yueling3
2009-07-01
Source PublicationJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
ISSN0021-7824
Volume92Issue:1Pages:18-51
AbstractThe Cauchy problem of the one-dimensional generalized Ginzburg-Landau (GGL) equation is considered. The local well-posedness is obtained for initial data in H(s)(R) with s > 0, and global result in H(s)(R) with s > 0 is also obtained under some conditions. Moreover, the relation between the solution for GGL equation and the solution for the derivative nonlinear Schrodinger (DNLS) equation is studied. It is proved that for some T > 0, the solution of Cauchy problem for the GGL equation converge to the solution of Cauchy problem for the DNLS in the natural space C([0, T]; H(s)) with s > 1/2 if some coefficients tend to zero. Moreover, if initial data belong to H(2), the convergence holds in C([0, T]; H(1)) for any T > 0. (c) 2009 Elsevier Masson SAS. All rights reserved.
KeywordGeneralized 1D Ginzburg-Landau equation Derivative nonlinear Schrodinger equation Well-posedness Inviscid limit behavior
DOI10.1016/j.matpur.2009.04.003
Language英语
Funding ProjectNSF of China[10601006] ; NSF of China[10701013] ; Department of Mathematics of City University of Hong Kong
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000268409300002
PublisherGAUTHIER-VILLARS/EDITIONS ELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/8869
Collection数学所
Corresponding AuthorHuo, Zhaohui
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
2.City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
3.Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China
Recommended Citation
GB/T 7714
Huo, Zhaohui,Jia, Yueling. Well-posedness and inviscid limit behavior of solution for the generalized 1D Ginzburg-Landau equation[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2009,92(1):18-51.
APA Huo, Zhaohui,&Jia, Yueling.(2009).Well-posedness and inviscid limit behavior of solution for the generalized 1D Ginzburg-Landau equation.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,92(1),18-51.
MLA Huo, Zhaohui,et al."Well-posedness and inviscid limit behavior of solution for the generalized 1D Ginzburg-Landau equation".JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 92.1(2009):18-51.
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