Global small solutions of 2-D incompressible MHD system

doi:10.1016/j.jde.2015.06.034

	Global small solutions of 2-D incompressible MHD system
	Lin, Fanghua 1; Xu, Li2 ; Zhang, Ping3,4
	2015-11-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	259 期号:10 页码:5440-5485
摘要	In this paper, we consider the global wellposedness of 2-D incompressible magneto-hydrodynamical system with smooth initial data which is close to some non-trivial steady state. It is a coupled system between the Navier-Stokes equations and a free transport equation with a universal nonlinear coupling structure. The main difficulty of the proof lies in exploring the dissipative mechanism of the system. To achieve this and to avoid the difficulty of propagating anisotropic regularity for the free transport equation, we first reformulate our system (1.1) in the Lagrangian coordinates (2.19). Then we employ anisotropic Littlewood-Paley analysis to establish the key a priori L-1(R+; Lip(R-2)) estimate for the Lagrangian velocity field Y-t. With this estimate, we can prove the global wellposedness of (2.19) with smooth and small initial data by using the energy method. We emphasize that the algebraic structure of (2.19) is crucial for the proofs to work. The global wellposedness of the original system (1.1) then follows by a suitable change of variables. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Inviscid MHD system Anisotropic Littlewood-Paley theory Dissipative estimates Lagrangian coordinates
DOI	10.1016/j.jde.2015.06.034
语种	英语
资助项目	NSF[DMS 1065964] ; NSF[DMS 1159313] ; National Center for Mathematics and Interdisciplinary Sciences ; NSF of China[11201455] ; NSF of China[10421101] ; NSF of China[10931007] ; Chinese Academy of Sciences[GJHZ200829]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000360258000018
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20659
专题	计算数学与科学工程计算研究所数学所
通讯作者	Zhang, Ping
作者单位	1.NYU, Courant Inst, New York, NY 10012 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lin, Fanghua,Xu, Li,Zhang, Ping. Global small solutions of 2-D incompressible MHD system[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2015,259(10):5440-5485.
APA	Lin, Fanghua,Xu, Li,&Zhang, Ping.(2015).Global small solutions of 2-D incompressible MHD system.JOURNAL OF DIFFERENTIAL EQUATIONS,259(10),5440-5485.
MLA	Lin, Fanghua,et al."Global small solutions of 2-D incompressible MHD system".JOURNAL OF DIFFERENTIAL EQUATIONS 259.10(2015):5440-5485.