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.