| Abstract: |
| We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a
bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the
problem based on a combination of the approach proposed by Judakov with a suitable form
of energy inequality. We show that global in time dissipative solutions always exist as long
as the rigid bodies are connected compact sets. In addition, in the absence of external driving
forces, the system always tends to a static equilibrium as time goes to infinity. The results
hold independently of possible collisions of rigid bodies and for any finite energy initial data. |
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