报告人: 丁时进 华南师范大学数学科学学院二级教授、博士生导师
报告时间：11月11日上午10：00-11：00
地点：36-507
Abstract: In this talk, we will introduce our recent results about the hydrodynamic stability for the 2-D plane Poiseuille flow $(1-y^2, 0)$ with Navier-slip boundary conditions in a periodic channel. For the linearized Navier-Stokes equations around the 2-D Poiseuille flow, the enhanced dissipation is obtained by using the careful resolvent estimates. For the nonlinear stability transition threshold, we prove that the solution of the Navier-Stokes equations around the 2-D Poiseuille flow does not transition away from the Poiseuille flow provided that the $H^1$ norm of the initial perturbation is less than the 3/4 power of the viscosity. The recent improvement from 3/4 to 2/3 is given by additional inviscid damping estimates. This part is based on the joint works with Zhilin Lin (JDE 2022, SCM 2025). The hydrodynamic stability and transition threshold are also given for plane Poiseuille flow $(1-y^2,0,0)$ with no-slip boundary conditions in 3-D periodic channel, jointly with Qi Chen, Zhilin Lin and Zhifei Zhang (Mem. Amer. Math. Soc., to appear).
报告人简介：丁时进，博士、华南师范大学二级教授、博士生导师、享受国务院政府特殊津贴专家。先后担任华南师范大学数学科学学院副院长、院长，大学人事处处长。现任华南师范大学华南数学应用与交叉研究中心常务副主任。先后主持国家自然科学基金面上项目6项、广东省自然科学基金面上项目5项、教育部博士点基金项目1项；参加国家973项目2项。2021年主持申报的“新型显示薄膜喷墨打印技术的数学建模与分析”获国家自然科学基金重点项目立项。发表论文70多篇，出版教材1部，出版专著1部。2012年被评为广东省南粤优秀教师，2015年获教育部自然科学二等奖。
