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

2025/05/07 by Bravin, Marco, Feireisl, Eduard, Roy, Arnab +1
#35B40 #35Q35 #74F10 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04372

Abstract

We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in R³. 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.

Citations

• Long-time behavior of an anisotropic rigid body interacting with a Poiseuille flow in an unbounded 2D channel
• On the Asymptotic Behavior in Time of the Kinetic Energy in a Rigid Body-Liquid Problem
• Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data
• Stabilization of a rigid body moving in a compressible viscous fluid

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