Global weak solutions to Landau-Lifshitz equations into compact Lie algebras

doi:10.1007/s11464-019-0803-7

	Global weak solutions to Landau-Lifshitz equations into compact Lie algebras
	Jia, Zonglin 2; Wang, Youde 1,3,4
刊名	FRONTIERS OF MATHEMATICS IN CHINA
	2019-12-16
页码	34
关键词	Landau-Lifshitz (LL) equations Lie algebra test functions
ISSN号	1673-3452
DOI	10.1007/s11464-019-0803-7
英文摘要	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.
资助项目	National Natural Science Foundation of China[11731001]
WOS研究方向	Mathematics
语种	英语
出版者	HIGHER EDUCATION PRESS
WOS记录号	WOS:000502589300002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50418]
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, Youde
作者单位	1.Guangzhou Univ, Coll Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China 2.China Acad Engn Phys, Inst Appl Phys & Computat Math, Beijing 100088, 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
推荐引用方式 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.