We present some properties of functions in suitable Sobolev spaces which arise naturally in the study of the motion of a rigid body in compressible and incompressible fluid. We relax the regularity assumption of the rigid body by allowing its boundary to be Lipschitz. In the case of a smooth rigid body we obtain a new estimate on the angular velocity. Our results extend and complement related results by V. Starovoitov and moreover we show that they are optimal. As an application we present an example where the rigid body collides with the boundary with non zero speed. Finally, we present a new non collision result concerning a smooth rotating body approaching the boundary, without assuming any special geometry on either the body or the container.

我们介绍了在合适的Sobolev空间中函数的一些性质，这些性质是在研究可​​压缩和不可压缩流体中刚体运动时自然产生的。我们通过允许刚体的边界为Lipschitz来放松刚体的正则性假设。在光滑刚体的情况下，我们获得了对角速度的新估计。我们的结果扩展和补充了V. Starovoitov的相关结果，此外，我们证明了它们是最优的。作为一个应用，我们给出一个例子，其中刚体以非零速度与边界碰撞。最后，我们提出了一个新的非碰撞结果，涉及到一个光滑的旋转物体接近边界，而没有在物体或容器上假设任何特殊几何形状的情况。