We consider optimal control problems of systems governed by quasi-linear, stationary, incompressible Navier–Stokes equations with shear-dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of viscosity functions with shear-thinning behaviour. Our aim is to prove the existence of a solution for the class of control problems and derive the first order optimality conditions.

CEMAT - Center for Computational and Stochastic Mathematics