On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium

doi:10.1002/cpa.21645

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	On the Global Solution of a 3-D MHD System with Initial Data near Equilibrium
	Abidi, Hammadi 1; Zhang, Ping2,3
	2017-08-01
发表期刊	COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN	0010-3640
卷号	70 期号:8 页码:1509-1561
摘要	In 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.
DOI	10.1002/cpa.21645
语种	英语
资助项目	National Center for Mathematics and Interdisciplinary Sciences ; National Science Foundation[11371037]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000403446800003
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25654
专题	数学所
通讯作者	Abidi, Hammadi
作者单位	1.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
推荐引用方式 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.