On the uniqueness of the optimal control for 2-dimensional second grade fluids

We study an optimal control problem with a quadratic cost functional for non-Newtonian fluids of differential type. More precisely, we consider the system governing the evolution of a second grade fluid filling a two-dimensional bounded domain, supplemented with a Navier slip boundary condition, and under certain assumptions on the size of the initial data and parameters of the model, we prove the second-order sufficient optimality conditions. Furthermore, we establish a global uniqueness result for the solutions of the first-order optimality system.