We perform a mathematical analysis of the steady flow of a viscous liquid, \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{L}}$$\end{document} , past a three-dimensional elastic body, \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{B}}$$\end{document} . We assume that \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{L}}$$\end{document} fills the whole space exterior to \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{B}}$$\end{document} , and that its motion is governed by the Navier–Stokes equations corresponding to non-zero velocity at infinity, v∞. As for \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{B}}$$\end{document} , 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 \documentclass[12pt]{minimal}
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\begin{document}$${\mathcal{B}}$$\end{document} 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.
