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Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations
Hao, Chengchun1,2; Luo, Tao3
2021-10-25
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume299Pages:542-601
AbstractThe 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.
KeywordIncompressible ideal magnetohydrodynamics equations Linearized equations Free boundary problem Local well-posedness
DOI10.1016/j.jde.2021.07.030
Indexed BySCI
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000686058600017
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/59096
Collection中国科学院数学与系统科学研究院
Corresponding AuthorHao, Chengchun
Affiliation1.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
Recommended Citation
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.
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