Distributed control for shear-thinning non-Newtonian fluids

Journal of Mathematical Fluid Mechanics, 14(4) (2012), 771-789
http://dx.doi.org/10.1007/s00021-012-0101-6

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.