Work

On blow-up trees for the harmonic map heat flow from $$B^2$$ to $$S^2$$

Year: 2026

Type: article

Abstract: We consider finite-time and k -equivariant solutions to the harmonic map heat flow from $$B^2$$ B 2 to $$S^2$$ S 2 under general time-dependent boundary data and prove that the bubble tree decomposition contains only one bubble. The method relies on the Maximum and Comparison Principle. We also exhibit solutions blowing up in infinite time for any $$k \ge 1$$ k ≥ 1 .

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-026-03396-0

Author: Dylan Samuelian

Institution: École Polytechnique Fédérale de Lausanne

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: École Polytechnique Fédérale de Lausanne