A Persistent Two-Bubble Solution for the 2-Equivariant Harmonic-Map Heat Flow
Year: 2026
Type: preprint
Abstract: We construct a family of smooth finite-energy 2-equivariant harmonic-map heat-flow solutions in the topological sector (0,2) which are global and admit an asymptotic decomposition into two well-separated harmonic maps with a remainder converging to zero in the reduced energy topology. For sufficiently small ε > 0, the initial datum is an explicitly corrected two-bubble profile with canonical scales λ(0) = ε and μ(0) = 1. The proof combines a quantitative Bogomolny trapping theorem, a fully gauge-restored first elliptic interaction corrector, adaptive two-chart spacetime coercivity, a finite-horizon renormalized inner current, and an outer renormalized Hasimoto normal form. The outer scale converges to a finite non-zero limit μ∞,ε = 1 + o(1), while the inner scale satisfies lim_{t→∞} (1/t) log(λ(t)/λ(0)) = −16/(π μ∞,ε²). The coefficient 16/π is generated by the exact Fredholm projection of the nearest-neighbour two-bubble interaction. The Jendrej–Lawrie continuous equivariant bubble-decomposition theorem is used only after global existence has been established, to identify the final number and signs of bubbles and to obtain convergence of the canonical remainder.
Author: Hwang, Jaegue
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7210262517
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