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September 5, 2026Open Access

An Unconditional Persistent Two-Bubble Solution for the 2-Equivariant Harmonic-Map Heat Flow

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Authors

JHJaegue Hwang

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Overview

Theoretical analysis reveals global persistent two-bubble solutions in 2-equivariant harmonic-map heat flow, indicating infinite-time scale separation without prior regime assumptions.

Key Points

  • To construct smooth, finite-energy solutions to the 2-equivariant harmonic-map heat flow in topological sector (0,2) that unconditionally exhibit a persistent two-bubble regime.
  • Constructed initial profiles with explicit interaction correctors and canonical scales λ(0) = ε and μ(0) = 1 for sufficiently small ε > 0.
  • Combined quantitative Bogomolny trapping, adaptive two-chart coercivity, and a renormalized outer Hasimoto normal form to close bootstrap bounds and exclude finite-time singularities.
  • Demonstrated global solutions admitting the asymptotic bubble decomposition u(t) = Q_λ(t) + Q_μ(t) + g(t) with energy residual ||g(t)||_E → 0.
  • Showed the outer bubble scale stabilizes to a finite non-zero value μ_infinity,ε while the inner scale λ(t) shrinks exponentially at the precise rate lim_{t→∞} [(1/t) log(λ(t)/λ(0))] = −16 / (π μ_infinity,ε²).

Cite This Study

Jaegue Hwang (2026) studied this question.

synapsesocial.com/papers/6a9bd4346b95aff0620ebb51https://doi.org/10.5281/zenodo.22280652
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  1. 1A Persistent Two-Bubble Solution for the 2-Equivariant Harmonic-Map Heat Flow2026
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  4. 4Radiation Memory and Refined Scale-Interaction Laws in a Persistent Two-Bubble Regime of the 2-Equivariant Harmonic-Map Heat Flow2026
  5. 5Radiation Memory and Nearest-Neighbor Drift in a Persistent Two-Bubble Regime of the 2-Equivariant Harmonic-Map Heat Flow2026