On the long-time behaviour of a rigid body immersed in a viscous fluid

Abstract

We consider the motion of a single rigid ball in a bounded 2D-domain under the action of the gravitational force. We show that the position of the ball stabilizes to a single equilibrium as time tends to infinity provided the boundary of the domain does not contain ‘flat’ parts perpendicular to the vertical direction.

Keywords:

• rigid body
• viscous fluid
• Navier–Stokes system

AMS Subject Classification::

• 35Q30

Acknowledgements

The work of EF was supported by Grant 201/09/0917 of GA ČR and of ŠN by Grant IAA100190804 of GA ASCR in the framework of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.