On the stationary Navier-Stokes flows around a rotating body

Consider the stationary motion of an incompressible Navier-Stokes fluid around a rotating body K = ℝ ³\Ω which is also moving in the direction of the axis of rotation. We assume that the translational and angular velocities U,ω are constant and the external force is given by f = div F. Then the motion is described by a variant of the stationary Navier-Stokes equations on the exterior domain Ω for the unknown velocity u and pressure p, with U, ω, F being the data. We first prove the existence of at least one solution (u, p) satisfying ∇u, p ∈ L _3/2,∞(Ω) and u ∈ L _3,∞(Ω) under the smallness condition on {pipe}U{pipe} + {pipe}ω{pipe} + {double pipe}F{double pipe} _L3/2,∞(Ω). Then the uniqueness is shown for solutions (u, p) satisfying ∇u, p ∈ L _3/2,∞(Ω) ∩ L _q,r(Ω) and u ∈ L _3,∞(Ω) ∩ L _q*,r(Ω) provided that 3/2 < q < 3 and F ∈ L _3/2,∞(Ω) ∩ L _q,r(Ω). Here L _q,r(Ω) denotes the well-known Lorentz space and q* = 3q/(3 - q) is the Sobolev exponent to q.