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Global weak solutions to Landau-Lifshitz equations into compact Lie algebras
Jia, Zonglin1; Wang, Youde2,3,4
2019-12-16
Source PublicationFRONTIERS OF MATHEMATICS IN CHINA
ISSN1673-3452
Pages34
AbstractWe 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.
KeywordLandau-Lifshitz (LL) equations Lie algebra test functions
DOI10.1007/s11464-019-0803-7
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11731001]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000502589300002
PublisherHIGHER EDUCATION PRESS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50419
Collection中国科学院数学与系统科学研究院
Corresponding AuthorWang, Youde
Affiliation1.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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