Steady flow of a Navier-stokes liquid past an elastic body

We perform a mathematical analysis of the steady flow of a viscous liquid, L, past a three-dimensional elastic body, B. We assume that L fills the whole space exterior to B, and that its motion is governed by the Navier-Stokes equations corresponding to non-zero velocity at infinity, v_∞. As for B, we suppose that it is a St. Venant-Kirchhoff material, held in equilibrium either by keeping an interior portion of it attached to a rigid body or by means of appropriate control body force and surface traction. We treat the problem as a coupled steady state fluid-structure problem with the surface of B as a free boundary. Our main goal is to show existence and uniqueness for the coupled system liquid-body, for sufficiently small v_∞ This goal is reached by a fixed point approach based upon a suitable reformulation of the Navier-Stokes equation in the reference configuration, along with appropriate a priori estimates of solutions to the corresponding Oseen linearization and to the elasticity equations.