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

doi:10.1007/s11464-019-0803-7

CSpace

	Global weak solutions to Landau-Lifshitz equations into compact Lie algebras
	Jia, Zonglin 1; Wang, Youde 2,3,4
	2019-12-16
发表期刊	FRONTIERS OF MATHEMATICS IN CHINA
ISSN	1673-3452
页码	34
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.
关键词	Landau-Lifshitz (LL) equations Lie algebra test functions
DOI	10.1007/s11464-019-0803-7
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11731001]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000502589300002
出版者	HIGHER EDUCATION PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50419
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.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
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.