Most studies on fluid dynamics have been devoted to Newtonian fluids, which are characterized by the classical Newton’s law of viscosity. However, there exists many real fluids with nonlinear viscoelastic behavior that does not obey Newton’s law of viscosity. My aim is to present some results on the derivation of "the optimality system" related to a class of non-Newtonian fluids of differential type. Namely, the optimal control of deterministic incompressible 3rd-grade fluids in 2D, via formal Lagrange multipliers in infinite-dimensional systems and the stochastic optimal control of the 2D/3D 3rd-grade fluids driven by a multiplicative noise.

This talk is based on a recent works with Fernanda Cipriano (CMA, Univ. NOVA de Lisboa).