论文标题
在2D通道中，Navier-Stokes周期性流量的最小时间内的确切可控性
Exact controllability in minimal time of the Navier-Stokes periodic flow in a 2D-channel
论文作者
论文摘要
这项工作与最小的时间控制问题$（p）$相关的最佳条件涉及2D通道中的线性化navier-Stokes周期性流量，但要受到速度横向组件的边界输入。这个问题的目的是在最短的时间内达到层流制度，以及在此之后的保存。确定必要的最佳条件依赖于对傅立叶模式的中间时间控制问题的分析$（p_ {k}）$与Navier-Stokes方程相关的傅立叶模式$“ k” $以及对其最大原则的证明。还发现，一个人可以根据问题的最佳控制器$（p_ {k}），$ shine称为\ textit {quasasi minimal}和边界控制器，在$％（p）中实现所需目标。$。
This work is concerned with the necessary conditions of optimality for a minimal time control problem $(P)$ for the linearized Navier-Stokes periodic flow in a 2D-channel, subject to a boundary input which acts on the transversal component of the velocity. The objective in this problem is the reaching of the laminar regime in a minimum time, as well as its preservation after this time. The determination of the necessary conditions of optimality relies on the analysis of intermediate minimal time control problems $(P_{k})$ for the Fourier modes $"k"$ associated to the Navier-Stokes equations and on the proof of the maximum principle for them. Also it is found that one can construct, on the basis of the optimal controllers of problems $(P_{k}),$ a small time called here \textit{quasi minimal} and a boundary controller which realizes the required objective in $% (P).$
