Equivariant wave maps on the hyperbolic plane with large energy
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Author(s)
Oh, Sung-Jin
Shahshahani, Sohrab
Lawrie, Andrew W
Date Issued
July 2017
Journal
Mathematical Research Letters
Publisher
International Press of Boston
Citation
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
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4310/MRL.2017.V24.N2.A10
