讲座题目： Infinite time bubbling for the SU(2) Yang-Mills heat flow on $\mathbb{R}^4$

主办单位：三峡数学研究中心

报告专家：郑有泉 副教授

报告时间： 2022年4月8日9:00-12:00

报告地点： 腾讯会议（ID: 286-561-218）

专家简介：郑有泉，2011年博士毕业于南开大学，现为天津大学数学学院副教授；主要研究领域为非线性椭圆与抛物型偏微分方程，担任面上项目、青年基金项目，教育部博士点基金项目主持人；主要研究结果发表在AJM, Math. Ann., JDE, JFA, CVPDE等期刊上。

报告摘要：We investigate the long time behaviour of the Yang-Mills heat flow on the bundle $\mathbb{R}^4\times SU(2)$. Waldron proved global existence and smoothness of the flow in this setting, leaving open the issue of the behaviour at infinity. 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 $\mathbb R^4$. 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. This is a joint work with Yannick Sire and Juncheng Wei.