On the Steady Motion of a Coupled System Solid-Liquid

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