报 告 人：张平 研究员 中国科学院
腾讯会议ID：666 511 840
报告时间： 2021-3-26(周五) 15:00-16:00
报 告 题目（一）：Global existence and decay of solutions to Prandtl system with small analytic and Gevrey data
摘要：In this paper, we prove the global existence and the large time decay estimate of solutions to Prandtl system with small initial data, which is analytical in the tangential variable. The key ingredient used in the proof is to derive sufficiently fast decay-in-time estimate of some weighted analytic energy estimate to a quantity, which consists of a linear combination of the tangential velocity with its primitive one, and which basically controls the evolution of the analytical radius to the solutions. Our result can be viewed as a global-in-time Cauchy-Kowalevsakya result for Prandtl system with small analytical data, which in particular improves the previous result in \cite{IV16} concerning the almost global well-posedness of two-dimensional Prandtl system. Finally I'll present our recent result concerning the global wellposedness with small Gevrey data. This is a partially joint work with N. Liu; M. Paicu; C. Wang and Y. Wang.
报告时间：2021-3-27(周六) 9:00-10:00
报 告 题目（二）：Global well-posedness of 3-D anisotropic Navier-Stokes system with large vertical viscous coefficient
摘要：In this paper, we first prove the global well-posedness of 3-D anisotropic Navier-Stokes system
provided that the vertical viscous coefficient of the system is sufficiently large compared to some critical norm of the initial data. Then we shall construct a family of initial data, u0,ν, which vary fast enough in the vertical variable and which can be arbitrarily large in the space $BMO^{-1}$. Yet $u_{0,\nu}$ still generates a unique global solution to the classical 3-D Navier-Stokes system provided that $\nu$ is sufficiently large.
报告人简介：张平，现任中科院数学与系统科学研究院研究员，数学研究所所长。曾2005年获国家杰出青年科学基金；2007年获第十届中国青年科技奖; 2011年获国家自然科学二等奖；2019年获中国数学会陈省身奖等奖项。自1997年以来，共在Comm. Pure Appl. Math.，Ann. Sci. École Norm. Sup. , Arch. Ration. Mech. Anal.， Comm. Math. Phys.，Adv. Math.， J. Reine Angew. Math.等杂志发表文章100余篇，在美国数学会出版专著一本。主要研究领域为粘性不可压缩流体力学方程组与非线性Schraedinger方程的半经典极限。
欢迎各位老师和同学参加！
