KMS Of Academy of mathematics and systems sciences, CAS
| 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 Publication | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS
 |
| ISSN | 1548-159X |
| Volume | 15Issue:4Pages:283-336 |
| Abstract | 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. |
| Keyword | wave map equation hyperbolic spaces asymptotic stability harmonic maps curved spacetime |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000452189000003 |
| Publisher | INT PRESS BOSTON, INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31953 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Li, Ze |
| Affiliation | 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 |
| 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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