  In this paper we consider a fluid-structure interaction problem given by the
steady Navier Stokes equations coupled with linear elasticity taken from
[Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An
elastic body surrounded by a liquid in a rectangular domain is deformed by the
flow which can be controlled by the Dirichlet boundary condition at the inlet.
On the walls along the channel homogeneous Dirichlet boundary conditions and on
the outflow boundary do-nothing conditions are prescribed. We recall existence
results for the nonlinear system from that reference and analyze the control to
state mapping generalizing the results of [Wollner and Wick, J. Math. Fluid
Mech., 21, 2019] to the setting of the nonlinear Navier-Stokes equation for the
fluid and the situation of mixed boundary conditions in a domain with corners.
