Stability of equilibria and bifurcations for a fluid-solid interaction problem

We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is driven by a uniform flow at spatial infinity, with constant dimensionless velocity lambda. We show that if lambda is below a critical value, lambda(c )(say), there is a unique and stable time-independent configuration, where the body is in equilibrium and the flow is steady. We also prove that, if lambda < lambda(c) , no oscillatory flow may occur. Successively, we investigate possible loss of uniqueness by providing necessary and sufficient conditions for the occurrence of a steady bifurcation at some lambda(s) >= lambda (c) . (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).