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arXiv · 2505.04372

On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid

Marco Bravin·Eduard Feireisl·Arnab Roy·Arghir Zarnescu
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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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Marco Bravin, Eduard Feireisl, Arnab Roy, Arghir Zarnescu. 2025-05-07. On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid. https://arxiv.org/abs/2505.04372

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