  The aim of this work is to study the optimal control problems of flows
governed by the incompressible third grade fluid equations with Navier-slip
boundary conditions. After recalling a result on the well-posedness of the
state equations, we study the existence and the uniqueness of solution to the
linearized state and adjoint equations. Furthermore, we present a stability
result for the state, and show that the solution of the linearized equation
coincides with the G\^ateaux derivative of the control-to-state mapping. Next,
we prove the existence of an optimal solution and establish the first order
optimality conditions. Finally, an uniqueness result of the coupled system
constituted by the state equation, the adjoint equation and the first order
optimality condition is established, under sufficiently large intensity of the
cost.
