  We study the long-time behavior of an elliptic rigid body which is allowed to
vertically translate and rotate in a 2D unbounded channel under the action of a
Poiseuille flow at large distances. The motion of the fluid is modelled by the
incompressible Navier-Stokes equations, while the motion of the solid is
described through Newton's laws. In addition to the solid inertia and the
hydrodynamic forces, we assume the dynamics of the solid is driven by internal
elastic restoring forces but without any structural damping. Through a precise
description of the motion of the elliptic body whenever it comes close to the
channel boundaries, we prove global-in-time existence of weak solutions. Our
second main contribution is a proof of return to equilibrium in case the
amplitude of the Poiseuille flow is small. \black To our knowledge, this
represents the first long-time analysis of fluid-solid interaction problems
with a given non-trivial final state.
