Well-posedness and inviscid limit behavior of solution for the generalized 1D Ginzburg-Landau equation | |
Huo, Zhaohui1,2; Jia, Yueling3 | |
2009-07-01 | |
Source Publication | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES |
ISSN | 0021-7824 |
Volume | 92Issue:1Pages:18-51 |
Abstract | The 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. |
Keyword | Generalized 1D Ginzburg-Landau equation Derivative nonlinear Schrodinger equation Well-posedness Inviscid limit behavior |
DOI | 10.1016/j.matpur.2009.04.003 |
Language | 英语 |
Funding Project | NSF of China[10601006] ; NSF of China[10701013] ; Department of Mathematics of City University of Hong Kong |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000268409300002 |
Publisher | GAUTHIER-VILLARS/EDITIONS ELSEVIER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/8869 |
Collection | 数学所 |
Corresponding Author | Huo, Zhaohui |
Affiliation | 1.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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