报告题目： Rigidity of the Navier-Stokes equations

报告人:  雷震， 复旦大学

时 间: 2019年8月6日10:30

地 点: 英国威廉希尔公司一楼报告厅

摘要：It has been an old and challenging problem to classify bounded ancient solutions of the incompressible Navier-Stokes equations, which could play a crucial role in the study of global regularity theory.

In the works (see the references), the authors made the following conjecture:

\textit{for the 3D axially symmetric Navier Stokes equations, bounded mild ancient solutions are constants}. In this article, we solve this conjecture in the case that $u$ is periodic in $z$. To the best of our knowledge, this seems to be the first result on this conjecture without unverified decay conditions. It also shows that nontrivial periodic solutions are not models of possible singularities or high velocity regions. Some partial results in the non-periodic case is also given.

专家简介：

雷震，复旦大学数学科学学院教授，博士生导师，副经理。曾为美国普林斯顿高等研究院member，雷震教授的主要研究方向为偏微分方程及其控制理论。他提出了“强零条件”的概念，独立证明了二维不可压弹性力学方程平衡态附近经典解的整体存在性。曾获全国百篇优秀博士论文、上海市自然科学牡丹奖，国家自然科学基金优秀青年基金、中组部青年拔尖人才、教育部青年特聘教授、国家自然科学基金委杰出青年基金。