  We consider the problem of a body moving within an incompressible fluid at
constant speed parallel to a wall, in an otherwise unbounded domain. This
situation is modeled by the incompressible Navier-Stokes equations in an
exterior domain in a half space, with appropriate boundary conditions on the
wall, the body, and at infinity. We focus on the case where the size of the
body is small. We prove in a very general setup that the solution of this
problem is unique and we compute a sharp decay rate of the solution far from
the moving body and the wall.
