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--- 分析与偏微分方程讨论班(2022春季第10讲)

题目: Smooth controllability of the incompressible Navier-Stokes equation with Navier boundary conditions

报告人: 廖家江 （北京应用物理与计算数学研究所）

时间：2022-5-17   14：00-15：00  (周二下午)  

地点: #腾讯会议：141-623-295  

https://meeting.tencent.com/dm/2E4v2v6IsBuU  

摘要: We deal with the 3D Navier–Stokes equation in a smooth simply connected bounded domain, with controls on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the remaining, uncontrolled, part of the boundary. We extend the small-time global exact null controllability result in Coron et al. (J Eur Math Soc 22:1625–1673, 2020) from Leray weak solutions to the case of smooth solutions. Our strategy relies on a refifinement of the method of well-prepared dissipation of the viscous boundary layers which appear near the uncontrolled part of the boundary, which allows to handle the multi-scale features in a fifiner topology. As a byproduct of our analysis we also obtain a small-time global approximate Lagrangian controllability result.

报告人简介: 廖家江，本科毕业于复旦大学，博士毕业于中国科学院数学与系统科学研究院。主要研究流体力学方程组的边界控制问题。曾获得第四届全国PDE博士生论坛优秀论文奖。

邀请人：郑孝信

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