The steady Navier-Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain

摘要

We assume that Ω is a bounded domain in IR~2 with N holes. We study the steady Navier-Stokes problem with inhomogeneous Navier-type boundary conditions in Ω (problem BVP-1) and the two other related problems BVP-2 and BVP-3. We prove the existence of strong solutions of BVP-2 and BVP-3 and the uniqueness of solutions for "small data". The existence of a strong solution of BVP-1 is proven only if the body force f belongs to a certain set m(IR~N). We show that problem BVP-1 is not solvable for some configurations of given boundary data and body forces.