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Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case
Li, Ze1; Ma, Xiao2; Zhao, Lifeng2
2018
Source PublicationDYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
ISSN1548-159X
Volume15Issue:4Pages:283-336
AbstractIn 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.
Keywordwave map equation hyperbolic spaces asymptotic stability harmonic maps curved spacetime
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000452189000003
PublisherINT PRESS BOSTON, INC
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31953
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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