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 ΩΩ of R3R3 of class C1C1. We show that, if the boundary datum belongs to Lq(∂Ω)Lq(∂Ω), q>3/2q>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.