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 B² to S²

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arxiv 2507.23583 v2 pith:VMQTJ2RD submitted 2025-07-31 math.AP

On blow-up trees for the harmonic map heat flow from B² to S²

Dylan Samuelian This is my paper

classification math.AP

keywords bubbleflowharmonicheatsolutionsblow-upblowingboundary

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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 $k \geq 1$.

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Nonexistence of finite-time blow-up for the equivariant harmonic map heat flow from $B^2$ to $S^2$
math.AP 2026-06 unverdicted novelty 7.0

Proves nonexistence of finite-time blow-up for D-equivariant harmonic map heat flow from B² to S² when D ≥ 3 under general smooth time-dependent boundary data.