This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) - uDelta u + (u cdot abla)u + abla_p = f in Omega $$ and $$ (1.2) ubla cdot u = 0 in Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on Gamma_0 _{g on Gamma_g, $$ where $Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $Gamma = partialOmega$, which is composed of two disjoint parts $Gamma_0$ and $Gamma_g$.