Equivariant wave maps on the hyperbolic plane with large energy
In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space H² into surfaces of revolution N that was initiated in [12, 13]. When the target N = H² we proved in [12] the existence and asymptotic stability of a 1-parameter family of finite energy harmonic maps...
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| Format: | Article |
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International Press of Boston
2018
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| Online Access: | http://hdl.handle.net/1721.1/115853 https://orcid.org/0000-0002-9579-5760 |
| _version_ | 1826216657835524096 |
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| author | Oh, Sung-Jin Shahshahani, Sohrab Lawrie, Andrew W |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Oh, Sung-Jin Shahshahani, Sohrab Lawrie, Andrew W |
| author_sort | Oh, Sung-Jin |
| collection | MIT |
| description | In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space H² into surfaces of revolution N that was initiated in [12, 13]. When the target N = H² we proved in [12] the existence and asymptotic stability of a 1-parameter family of finite energy harmonic maps indexed by how far each map wraps around the target. Here we conjecture that each of these harmonic maps is globally asymptotically stable, meaning that the evolution of any arbitrarily large finite energy perturbation of a harmonic map asymptotically resolves into the harmonic map itself plus free radiation. Since such initial data exhaust the energy space, this is the soliton resolution conjecture for this equation. The main result is a verification of this conjecture for a nonperturbative subset of the harmonic maps. |
| first_indexed | 2024-09-23T16:51:18Z |
| format | Article |
| id | mit-1721.1/115853 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:51:18Z |
| publishDate | 2018 |
| publisher | International Press of Boston |
| record_format | dspace |
| spelling | mit-1721.1/1158532022-10-03T08:44:08Z Equivariant wave maps on the hyperbolic plane with large energy Oh, Sung-Jin Shahshahani, Sohrab Lawrie, Andrew W Massachusetts Institute of Technology. Department of Mathematics Lawrie, Andrew W In this paper we continue the analysis of equivariant wave maps from 2-dimensional hyperbolic space H² into surfaces of revolution N that was initiated in [12, 13]. When the target N = H² we proved in [12] the existence and asymptotic stability of a 1-parameter family of finite energy harmonic maps indexed by how far each map wraps around the target. Here we conjecture that each of these harmonic maps is globally asymptotically stable, meaning that the evolution of any arbitrarily large finite energy perturbation of a harmonic map asymptotically resolves into the harmonic map itself plus free radiation. Since such initial data exhaust the energy space, this is the soliton resolution conjecture for this equation. The main result is a verification of this conjecture for a nonperturbative subset of the harmonic maps. National Science Foundation (U.S.) (Grant DMS-1302782) National Science Foundation (U.S.) (Grant 1045119) 2018-05-24T17:24:48Z 2018-05-24T17:24:48Z 2017-07 2015-05 2018-05-24T15:47:24Z Article http://purl.org/eprint/type/JournalArticle 1073-2780 1945-001X http://hdl.handle.net/1721.1/115853 Lawrie, Andrew et al. “Equivariant Wave Maps on the Hyperbolic Plane with Large Energy.” Mathematical Research Letters 24, 2 (2017): 449–479 © 2017 International Press of Boston https://orcid.org/0000-0002-9579-5760 http://dx.doi.org/10.4310/MRL.2017.V24.N2.A10 Mathematical Research Letters Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf International Press of Boston arXiv |
| spellingShingle | Oh, Sung-Jin Shahshahani, Sohrab Lawrie, Andrew W Equivariant wave maps on the hyperbolic plane with large energy |
| title | Equivariant wave maps on the hyperbolic plane with large energy |
| title_full | Equivariant wave maps on the hyperbolic plane with large energy |
| title_fullStr | Equivariant wave maps on the hyperbolic plane with large energy |
| title_full_unstemmed | Equivariant wave maps on the hyperbolic plane with large energy |
| title_short | Equivariant wave maps on the hyperbolic plane with large energy |
| title_sort | equivariant wave maps on the hyperbolic plane with large energy |
| url | http://hdl.handle.net/1721.1/115853 https://orcid.org/0000-0002-9579-5760 |
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