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arXiv · 2601.21017

Global oscillatory solutions for the Yang-Mills heat flow

Yannick Sire·Juncheng Wei·Youquan Zheng·Yifu Zhou
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Abstract

We investigate the long-time dynamics for the global solution of the $SO(4)$-equivariant Yang-Mills heat flow (YMHF) with structure group $SU(2)$ in space dimension $4$. For a class of initial data with specific decay at spatial infinity, we prove that the long-time dynamics of YMHF can be described by the initial data in a unified manner. As a consequence, the global solutions can exhibit blow-up, blow-down, and more exotically, {\it oscillatory} asymptotic behavior at time infinity. This seems to be the first example of Yang-Mills heat flows with oscillatory behavior as $t\to \infty$.

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Yannick Sire, Juncheng Wei, Youquan Zheng, Yifu Zhou. 2026-01-28. Global oscillatory solutions for the Yang-Mills heat flow. https://arxiv.org/abs/2601.21017

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