Global small solutions of 2-D incompressible MHD system
文献类型：期刊论文
| 作者 | Lin, Fanghua1; Xu, Li2 ; Zhang, Ping3,4
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| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2015-11-15 |
| 卷号 | 259期号:10页码:5440-5485 |
| 关键词 | Inviscid MHD system Anisotropic Littlewood-Paley theory Dissipative estimates Lagrangian coordinates |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2015.06.034 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000360258000018 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20658]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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