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On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium
Abidi, Hammadi1; Zhang, Ping2,3
2017-08-01
Source PublicationCOMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN0010-3640
Volume70Issue:8Pages:1509-1561
AbstractIn this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magnetohydrodynamical system with initial data close enough to the equilibrium state, (e(3),0). Compared with previous works by Lin, Xu, and Zhang and by Xu and Zhang, here we present a new Lagrangian formulation of the system, which is a damped wave equation and which is nondegenerate only in the direction of the initial magnetic field. Furthermore, we remove the admissible condition on the initial magnetic field, which was required in the earlier works. By using the Frobenius theorem and anisotropic Littlewood-Paley theory for the Lagrangian formulation of the system, we achieve the global L-1-in-time Lipschitz estimate of the velocity field, which allows us to conclude the global existence of solutions to this system. In the case when the initial magnetic field is a constant vector, the large-time decay rate of the solution is also obtained.(c) 2016 Wiley Periodicals, Inc.
DOI10.1002/cpa.21645
Language英语
Funding ProjectNational Center for Mathematics and Interdisciplinary Sciences ; National Science Foundation[11371037]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000403446800003
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25654
Collection数学所
Corresponding AuthorAbidi, Hammadi
Affiliation1.Fac Sci Tunis, Dept Math, Campus Univ, Tunis 2092, Tunisia
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, HUA Loo Keng Key Lab Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Abidi, Hammadi,Zhang, Ping. On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,2017,70(8):1509-1561.
APA Abidi, Hammadi,&Zhang, Ping.(2017).On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium.COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,70(8),1509-1561.
MLA Abidi, Hammadi,et al."On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium".COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS 70.8(2017):1509-1561.
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