Global oscillatory solutions for the Yang-Mills heat flow
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914288969449472 |
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| author | Sire, Yannick Wei, Juncheng Zheng, Youquan Zhou, Yifu |
| author_facet | Sire, Yannick Wei, Juncheng Zheng, Youquan Zhou, Yifu |
| contents | 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 $t\to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global oscillatory solutions for the Yang-Mills heat flow Sire, Yannick Wei, Juncheng Zheng, Youquan Zhou, Yifu Analysis of PDEs Differential Geometry 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 $t\to \infty$. |
| title | Global oscillatory solutions for the Yang-Mills heat flow |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2601.21017 |