Stability of Equilibria and Bifurcations for a Fluid-Solid Interaction Problem

We study certain significant properties of the equilibrium configurations ofa rigid body subject to an undamped elastic restoring force, in the stream of aviscous liquid in an unbounded 3D domain. The motion of the coupled system isdriven by a uniform flow at spatial infinity, with constant dimensionlessvelocity λ. We show that if λ is below a critical value,λ_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, ifλ<λ_c, no oscillatory flow may occur. Successively, weinvestigate possible loss of uniqueness by providing necessary and sufficientconditions for the occurrence of a steady bifurcation at some λ_s≥λ_c.