论文标题
在带有液体缝隙的刚体的自由旋转上
On the free rotations of rigid bodies with a liquid-filled gap
论文作者
论文摘要
我们考虑了一个空心刚体所构成的系统，该系统包含一个均匀的刚性球，并让固体之间的间隙完全用粘性不可压缩的液体填充。我们研究整个系统的自由旋转，即仅由流体 - 固体系统惯性驱动的动作，一旦将初始角动量施加在整个系统上。我们证明了全球弱解决方案和运动方程方程的强大解决方案的存在。此外，我们证明，随着时间的时间接近无限，流体速度以及内核角速度相对于外部固体收敛到零。
We consider the system constituted by a hollow rigid body whose cavity contains a homogeneous rigid ball, and let the gap between the solids be entirely filled by a viscous incompressible fluid. We investigate the free rotations of the whole system, i.e., motions driven only by the inertia of the fluid-solids system once an initial angular momentum is imparted on the whole system. We prove the existence of global weak solutions and local strong solutions to the equations of motion. In addition, we prove that the fluid velocity as well as the inner core angular velocity relative to the outer solid converge to zero as time approaches infinity.
