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September 2, 2026Open Access

Radiation Memory and Nearest-Neighbor Drift in a Persistent Two-Bubble Regime of the 2-Equivariant Harmonic-Map Heat Flow

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Authors

JHJaegue Hwang

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Overview

Theoretical analysis reveals radiation memory and deterministic drift govern bubble dynamics in two-equivariant harmonic-map heat flow, highlighting non-local scale evolution mechanisms.

Key Points

  • To characterize the late-time scale evolution and bubble interaction dynamics for the two-dimensional, 2-equivariant harmonic-map heat flow from R^2 to S^2 in a persistent two-bubble regime.
  • Analyzed a conditional late-time regime consisting of two well-separated harmonic-map bubbles with scales λ(t) ≪ μ(t) ≪ √t and vanishing energy remainder.
  • Constructed differentiable modulation parameters, isolated nearest-neighbor bubble interactions using an exact Fredholm projection, and applied a localized elliptic corrector.
  • Formulated closed radiation memory through a renormalized storage-flux balance and mapped it to the free heat evolution of a globally patched, profile-subtracted Hasimoto variable along an outer neck contour.
  • Determined that the leading deterministic drift rate of the inner bubble's logarithmic scale is -16σ/(π μ(t)^2), governed by relative orientation σ ∈ {±1}.
  • Demonstrated that the inner scale evolves as log(λ(t)/λ(T)) = M_rad^cl(T,t) - (16σ/π) ∫_T^t μ(s)^(-2) ds + o(∫_T^t μ(s)^(-2) ds), establishing that a critical order-one radiation memory persists at leading order.

Cite This Study

Jaegue Hwang (2026) studied this question.

synapsesocial.com/papers/6a97e305c562ede874ec78dbhttps://doi.org/10.5281/zenodo.22206602
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  1. 1Radiation Memory, Nearest-Neighbor Drift, and a Refined Logarithmic Interaction Law in a Persistent Two-Bubble Regime of the 2-Equivariant Harmonic-Map Heat Flow2026
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