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.