On the long-time behaviour of a system of several rigid bodies immersed in a viscous fluid
Abstract
We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in R 3 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.
Fields of Study & Subjects
Navier-Stokes equation solutions
Stability and Controllability of Differential Equations
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4823–4834
- Publication date
- 16 July 2026
- Language
- EN