We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an 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.
- Navier slip boundary conditions
- Navier-Stokes equations
- Optimal control