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Original Articles

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

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Pages 59-66 | Received 05 Feb 2010, Accepted 21 Feb 2010, Published online: 06 Jan 2011
 

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.

AMS Subject Classification::

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.

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