Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations

doi:10.1016/j.jde.2021.07.030

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	Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
	Hao, Chengchun 1,2; Luo, Tao 3
	2021-10-25
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	299 页码:542-601
摘要	The well-posedness theory is studied for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in Lagrangian coordinates, and substitute it into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, the velocity equation is linearized with respect to the position vector field whose time derivative is the velocity. In this formulation, a key idea is to use the Lie derivative of the magnetic field taking the advantage that the magnetic field is tangential to the free boundary and divergence free. This paper contributes to the program of developing geometric approaches to study the well-posedness of free boundary problems of ideal magnetohydrodynamics equations under the condition of Taylor sign type for general free boundaries not restricted to graphs. (c) 2021 Elsevier Inc. All rights reserved.
关键词	Incompressible ideal magnetohydrodynamics equations Linearized equations Free boundary problem Local well-posedness
DOI	10.1016/j.jde.2021.07.030
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11671384] ; National Natural Science Foundation of China[11971014] ; K. C. Wong Education Foundation ; Research Grants Council of Hong Kong[11305818]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000686058600017
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/59096
专题	中国科学院数学与系统科学研究院
通讯作者	Hao, Chengchun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, HLM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Hao, Chengchun,Luo, Tao. Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2021,299:542-601.
APA	Hao, Chengchun,&Luo, Tao.(2021).Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations.JOURNAL OF DIFFERENTIAL EQUATIONS,299,542-601.
MLA	Hao, Chengchun,et al."Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations".JOURNAL OF DIFFERENTIAL EQUATIONS 299(2021):542-601.