We consider the motion of a rigid body immersed in a two-dimensional viscous incompressible fluid with Navierslip-with-friction conditions at the solid boundary. The fluid-solid system occupies the whole plane. We provethe small-time exact controllability of the position and velocity of the solid when the control takes the form of adistributed force supported in a compact subset (with nonvoid interior) of the fluid domain, away from the body.The strategy relies on the introduction of a small parameter: we consider fast and strong amplitude controls forwhich the ``Navier-Stokes+rigid body'' system behaves like a perturbation of the ``Euler+rigid body'' system. Bythe means of a multi-scale asymptotic expansion we construct a controlled solution to the ``Navier-Stokes+rigidbody'' system thanks to some controlled solutions to ``Euler+rigid body''-type systems and to a detailed analysis ofthe influence of the boundary layer on the solid motion.

中文翻译：

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控制浸入二维粘性不可压缩流体中的刚体的运动距离

我们考虑浸入二维粘性不可压缩流体中的刚体的运动，在固体边界处具有 Navierslip-with-friction 条件。流固系统占据了整个平面。我们证明了当控制采用在流体域的紧凑子集（内部无空隙）中支持的分布式力的形式时，固体的位置和速度的小时间精确可控性，远离身体。 该策略依赖于介绍一个小参数：我们考虑快速和强振幅控制，“纳维-斯托克斯+刚体”系统表现得像“欧拉+刚体”系统的扰动。通过多尺度渐近展开，我们构建了“Navier-Stokes+rigidbody”的受控解