This paper is concerned with the boundary-value problem for the steady incompressible Navier-Stokes equations with damping. Two cases are considered here: 1) the Dirichlet's boundary condition; 2) the nonhomogeneous boundary condition. we obtain the existence and uniqueness of the weak solutions for the steady incompressible Navier-Stokes equations with damping using different methods for the above cases.
"Existence and Uniqueness of the Weak Solutions for the Steady Incompressible Navier-Stokes Equations with Damping." Afr. Diaspora J. Math. (N.S.) 12 (2) 57 - 72, 2011.