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

Dylan Samuelian

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

Analysis of PDEs 2025-08-01 v1

Authors: Dylan Samuelian

Abstract

We consider finite-time and $k$ -equivariant solutions to the harmonic map heat flow from $B^2$ to $S^2$ 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 $k \geq 1$ .

Keywords

harmonic map heat flow blow-up tree bubble tree decomposition Maximum Principle Comparison Principle

Cite

@article{arxiv.2507.23583,
  title  = {On blow-up trees for the harmonic map heat flow from $B^2$ to $S^2$},
  author = {Dylan Samuelian},
  journal= {arXiv preprint arXiv:2507.23583},
  year   = {2025}
}

Comments

89 pages, 1 figure

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