Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case

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	Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case
	Li, Ze 1; Ma, Xiao 2; Zhao, Lifeng 2
	2018
发表期刊	DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
ISSN	1548-159X
卷号	15 期号:4 页码:283-336
摘要	In this paper, we prove that the small energy harmonic maps from H-2 to H-2 are asymptotically stable under the wave map equation in the subcritical perturbation class. This result may be seen as an example supporting the soliton resolution conjecture for geometric wave equations without equivariant assumptions on the initial data. In this paper, we construct Tao's caloric gauge in the case when nontrivial harmonic map occurs. With the "dynamic separation" the master equation of the heat tension field appears as a semilinear magnetic wave equation. By the endpoint and weighted Strichartz estimates for magnetic wave equations obtained by the first author [38], the asymptotic stability follows by a bootstrap argument.
关键词	wave map equation hyperbolic spaces asymptotic stability harmonic maps curved spacetime
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000452189000003
出版者	INT PRESS BOSTON, INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31953
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Ze
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing, Peoples R China 2.Univ Sci & Technol China, Dept Math, Hefei, Anhui, Peoples R China
推荐引用方式 GB/T 7714	Li, Ze,Ma, Xiao,Zhao, Lifeng. Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case[J]. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,2018,15(4):283-336.
APA	Li, Ze,Ma, Xiao,&Zhao, Lifeng.(2018).Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case.DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS,15(4),283-336.
MLA	Li, Ze,et al."Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case".DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 15.4(2018):283-336.