Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	雷震教授，复旦大学数学科学学院
Inviter:
Title:	Rigidity of the Navier-Stokes equations
Time & Venue:	2019.4.27 9:30-10:30 N205
Abstract:	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: 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. 雷震，2006年博士毕业于复旦大学，现任复旦大学数学科学学院教授。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，在不可压缩的Navier-Stokes方程、高维非线性波动方程及其精确边界能控性理论等研究领域取得了国际领先的成果，被包括Bourgain、陶哲轩等十余位ICM报告人在内的同行SCI纯粹他引600余次，有5篇论文发表在CPAM上。雷震教授曾获上海市自然科学牡丹奖 (2014)、教育部自然科学一等奖(排第二、2011)、优青（2012首届）、杰青（2017）等荣誉。