On the Motion of Free Interface in Ideal Incompressible MHD

doi:10.1007/s00205-017-1082-7

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	On the Motion of Free Interface in Ideal Incompressible MHD
	Hao, Chengchun1,2,3
	2017-05-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	224 期号:2 页码:515-553
摘要	For the free boundary problem of the plasma-vacuum interface to 3D ideal incompressible magnetohydrodynamics, the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of view and some quantities such as the second fundamental form and the velocity of the free interface are estimated. In the vacuum region, the magnetic fields are described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic fields are tangential to the interface, but we do not need any restrictions on the size of the magnetic fields on the free interface. We introduce the "fictitious particle" endowed with a fictitious velocity field in vacuum to reformulate the problem to a fixed boundary problem under the Lagrangian coordinates. The L (2)-norms of any order covariant derivatives of the magnetic fields both in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall. The estimates of the curl of the electric fields in vacuum are also obtained, which are also indispensable in elliptic estimates.
DOI	10.1007/s00205-017-1082-7
语种	英语
资助项目	National Natural Science Foundation of China[11171327] ; National Natural Science Foundation of China[11671384] ; National Natural Science Foundation of China[11461161007] ; BCMIIS
WOS研究方向	Mathematics ; Mechanics
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000395182500005
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/225
专题	数学所
通讯作者	Hao, Chengchun
作者单位	1.Chinese Acad Sci, Inst Math, AMSS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Hao, Chengchun. On the Motion of Free Interface in Ideal Incompressible MHD[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2017,224(2):515-553.
APA	Hao, Chengchun.(2017).On the Motion of Free Interface in Ideal Incompressible MHD.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,224(2),515-553.
MLA	Hao, Chengchun."On the Motion of Free Interface in Ideal Incompressible MHD".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 224.2(2017):515-553.