On the Oseen and Navier–Stokes systems with a slip boundary condition

We consider the Robin problem for the Navier–Stokes equations in an exterior domain Ω of R 3 of class C 1 . We show that, if the boundary datum belongs to L q ( ∂ Ω ) , q > 3 / 2 , then there exists a solution of the problem which converges to an assigned constant vector at infinity and takes the boundary value in the sense of nontangential convergence.