This work deals with stochastic second grade fluids, which are incompressible non-Newtonian type fluids. It is well known that small random perturbations of turbulent fluids can substantially modify their behavior; here the deterministic equations are perturbed by a multiplicative white noise. We study the existence and uniqueness of stochastic solutions on a two-dimensional bounded domain endowed with slip boundary conditions. We also address a control problem, where the control is effected through a distributed random force.

The well-posedness of the corresponding linearized equations is the main issue to analyze the Gâteau derivative of the control-to-state map.

The analysis of stochastic backward adjoint equations allows to establish the first order necessary optimality conditions.