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Global small solutions of 2-D incompressible MHD system
Lin, Fanghua1; Xu, Li2; Zhang, Ping3,4
2015-11-15
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume259Issue:10Pages:5440-5485
AbstractIn 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.
KeywordInviscid MHD system Anisotropic Littlewood-Paley theory Dissipative estimates Lagrangian coordinates
DOI10.1016/j.jde.2015.06.034
Language英语
Funding ProjectNSF[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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000360258000018
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20659
Collection计算数学与科学工程计算研究所
数学所
Corresponding AuthorZhang, Ping
Affiliation1.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
Recommended Citation
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.
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