On a possibility of generalization of the Hopf lemma to the case of the Navier-Stokes system with nonzero flows

We examine the Hopf lemma (Leray inequality) which is used in proving the existence of a solution to a nonhomogeneous boundary value problem for the stationary Navier-Stokes equations of an incompressible fluid in a bounded domain. We study a possibility of generalization of a weakened variant of the lemma to the case of nonzero flows through the connected components of the boundary of the domain.