低雷诺数下刚体在不可压缩流体中的远程轨迹跟踪
Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number
摘要：
本文研究了在有界单连通区域内的定常不可压缩Stokes流中受牛顿定律驱动的刚体的运动。目的是通过控制流体域外边界上的狄利克雷边界数据的形式来跟踪固体的轨迹。我们表明，它是可能的，以准确地实现任何光滑的轨迹，远离外部边界的固体，通过这样的远程控制的手段。证明依赖于Stokes系统的一些密度方法，以及将固体方程转化为常微分方程。
英文摘要：
In this paper we study the motion of a rigid body driven by Newton's law immersed in a stationary incompressible Stokes flow occupying a bounded simply connected domain. The aim is that of trajectory tracking of the solid by the means of a control in the form of Dirichlet boundary data on the outside boundary of the fluid domain. We show that it is possible to exactly achieve any smooth trajectory for the solid that stays away from the external boundary, by the means of such a remote control. The proof relies on some density methods for the Stokes system, as well as a reformulation of the solid equations into an ODE.
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