PreprintCC BY 4.0arXiv
Stability of least-energy solutions of the harmonic map flow from the plane into the 2-sphere
Abstract
We prove the asymptotic stability of the least-energy harmonic map W:ℝ2→ S2 for the harmonic map flow under small, sufficiently decaying, non-symmetric perturbations. Solutions exist globally and are asymptotically described by a modulation of W plus a remainder that converges to zero as t→∞. The modulation parameters associated with scaling, rotation, and translation remain close to their initial values and converge to finite limits. The proof relies on an inner-outer gluing decomposition and the analysis of a non-local equation governing the modulation parameters.
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BibTeX
@misc{davila2026stability,
title = {{Stability of least-energy solutions of the harmonic map flow from the plane into the 2-sphere}},
author = {Juan Davila and Eliott Van Steirteghem},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01021},
eprint = {2611.01021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01021},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability of least-energy solutions of the harmonic map flow from the plane into the 2-sphere
AU - Juan Davila
AU - Eliott Van Steirteghem
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01021
UR - https://arxiv.org/abs/2611.01021
AB - We prove the asymptotic stability of the least-energy harmonic map W:ℝ^2→ S^2 for the harmonic map flow under small, sufficiently decaying, non-symmetric perturbations. Solutions exist globally and are asymptotically described by a modulation of W plus a remainder that converges to zero as t→∞. The modulation parameters associated with scaling, rotation, and translation remain close to their initial values and converge to finite limits. The proof relies on an inner-outer gluing decomposition and the analysis of a non-local equation governing the modulation parameters.
ER -