KMS Of Academy of mathematics and systems sciences, CAS
Global weak solutions to Landau-Lifshitz equations into compact Lie algebras | |
Jia, Zonglin1; Wang, Youde2,3,4 | |
2019-12-16 | |
Source Publication | FRONTIERS OF MATHEMATICS IN CHINA |
ISSN | 1673-3452 |
Pages | 34 |
Abstract | We consider a parabolic system from a bounded domain in a Euclidean space or a closed Riemannian manifold into a unit sphere in a compact Lie algebra g, which can be viewed as the extension of Landau-Lifshitz (LL) equation and was proposed by V. Arnold. We follow the ideas taken from the work by the second author to show the existence of global weak solutions to the Cauchy problems of such LL equations from an n-dimensional closed Riemannian manifold T or a bounded domain in Double-struck capital R-n into a unit sphere Sg\. In particular, we consider the Hamiltonian system associated with the non-local energy-micromagnetic energy defined on a bounded domain of Double-struck capital R-3 and show the initial-boundary value problem to such LL equation without damping terms admits a global weak solution. The key ingredient of this article consists of the choices of test functions and approximate equations. |
Keyword | Landau-Lifshitz (LL) equations Lie algebra test functions |
DOI | 10.1007/s11464-019-0803-7 |
Indexed By | SCI |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[11731001] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000502589300002 |
Publisher | HIGHER EDUCATION PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50419 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Wang, Youde |
Affiliation | 1.China Acad Engn Phys, Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China 2.Guangzhou Univ, Coll Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
Recommended Citation GB/T 7714 | Jia, Zonglin,Wang, Youde. Global weak solutions to Landau-Lifshitz equations into compact Lie algebras[J]. FRONTIERS OF MATHEMATICS IN CHINA,2019:34. |
APA | Jia, Zonglin,&Wang, Youde.(2019).Global weak solutions to Landau-Lifshitz equations into compact Lie algebras.FRONTIERS OF MATHEMATICS IN CHINA,34. |
MLA | Jia, Zonglin,et al."Global weak solutions to Landau-Lifshitz equations into compact Lie algebras".FRONTIERS OF MATHEMATICS IN CHINA (2019):34. |
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