  We consider a velocity tracking problem for the Navier-Stokes equations in a
2D-bounded domain. The control acts on the boundary through a injection-suction
device and the flow is allowed to slip against the surface wall. We study the
well-posedness of the state equations, linearized state equations and adjoint
equations. In addition, we show the existence of an optimal solution and
establish the first order optimality condition.

Analysis of PDEs