# Well-posedness and optimal control for stochastic second grade fluids

by Fernanda Cipriano (Dep. de Matemática da Univ. Nova de Lisboa)

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.