Optimal control of steady second grade fluids with a Navier-slip boundary condition

In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the viscoelastic parameter tends to zero, and prove that the corresponding sequence converges to a solution of an optimal control problem governed by the Navier-Stokes equations whose optimality conditions are recovered by passage to the limit.