KMS Of Academy of mathematics and systems sciences, CAS
| Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations | |
| Hao, Chengchun1,2; Luo, Tao3 | |
| 2021-10-25 | |
| Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| ISSN | 0022-0396 |
| Volume | 299Pages:542-601 |
| Abstract | 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. |
| Keyword | Incompressible ideal magnetohydrodynamics equations Linearized equations Free boundary problem Local well-posedness |
| DOI | 10.1016/j.jde.2021.07.030 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000686058600017 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59096 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Hao, Chengchun |
| Affiliation | 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 |
| 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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