中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

 

报告人:郑有泉 副教授 (天津大学)

 Infinite time bubbling for the SU(2) Yang-Mills heat flow on R^4

  2022.06.15(星期三)上午10:00-11:00

 点:腾讯会议948-3602-5762

  要:We investigate the long time behaviour of the Yang-Mills heat flow on the bundle R^4\times SU(2). Waldron proved global existence and smoothness of the flow on a compact connected 4-manifold, leaving open the issue of the behaviour at infinite time. We exhibit two types of long-time bubbling: first we construct an initial data and a globally defined solution which blows-up in infinite time at a given point in R^4. Second, we prove the existence of bubble-tower also in infinite time. This answers in definitive manner the basic properties of the heat flow of Yang-Mills connection in the critical dimension 4 and shows in particular that in general one cannot expect that this gradient flow converges to a Yang-Mills connection on 4-manifolds. We emphasize that we do not assume for the first result any symmetry assumption; whereas the second result on the existence of the bubble-tower is in the SO(4)-equivariant class, but nevertheless new. This is a joint work with Yannick Sire and Juncheng Wei.

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