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

We construct a family of smooth finite-energy global solutions of the 2-equivariant harmonic-map heat flow exhibiting a persistent concentric equal-sign two-bubble regime with separated scales. The outer scale converges to a finite nonzero limit, while the inner scale obeys an explicit universal leading interaction law with coefficient 16/π. This is Paper I of a three-paper series on the borderline 2-equivariant harmonic-map heat flow.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-15
DOI
https://doi.org/10.5281/zenodo.22761065
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

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

Jaegue Hwang
Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
preprint

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

Jaegue Hwang
preprint en

Abstract

We construct a family of smooth finite-energy global solutions of the 2-equivariant harmonic-map heat flow exhibiting a persistent concentric equal-sign two-bubble regime with separated scales. The outer scale converges to a finite nonzero limit, while the inner scale obeys an explicit universal leading interaction law with coefficient 16/π. This is Paper I of a three-paper series on the borderline 2-equivariant harmonic-map heat flow.

Zenodo (CERN European Organization for Nuclear Research)
The Seoul Institute (KR)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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A Persistent Two-Bubble Solution for the 2-Equivariant Harmonic-Map Heat Flow — Jaegue Hwang · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS