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【学术报告及分析与偏微分方程讨论班(2022春第10讲)】Smooth controllability of the incompressible Navier-Stokes equation with Navier boundary conditions
发布日期:2022-05-11  浏览量:

betway体育注册应用数学系学术报告

--- 分析与偏微分方程讨论班(2022春季第10)



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   1400-1500  (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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