On the free rotations of rigid bodies with a liquid-filled gap

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Mazzone, Giusy¹ 

[1] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

关键词: Fluid-solid interactions;    Navier-Stokes equations;    Rigid body motion;    Leray-Hopf weak solutions;    Critical spaces;    Strong solutions;   

DOI  :  10.1016/j.jmaa.2020.124826

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free