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

查看全文 作　　者：Zonglin [1]JIA;Youde [2,3,4]WANG

机构地区：[1]Institute of Applied Physics and Computational Mathematics,China Academy of Engineering Physics,Beijing 100088,China;[2]College of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China;[3]Hua Loo-Keng Key Laboratory of Mathematics,Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;[4]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Frontiers of Mathematics in China》索引2019年第14卷第6期,共34页

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.11731001). 摘　　要：We consider a parabolic system from a bounded domain in a Euclidean space or a closed Riernannian 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 Riernannian manifold T or a bounded domain in R^n into a unit sphere Sg(1)in g.In particular,we consider the Hamiltonian system associated with the nonlocal energy micromagnetic energy defined on a bounded domain of R^31 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

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

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