On the steady motion of a coupled system solid-liquid

We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B, L}, which means that there exists a frame with respect to which the relevant governing equations possess a timeindependent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.