Distributed control for multistate modified Navier-Stokes equations
Departamento de Matemática, Faculdade de Ciências e Tecnologia da
Universidade Nova de Lisboa, Quinta da Torre, 2829-516
Revised: 14 November 2011
The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality conditions.
Mathematics Subject Classification: 49K20 / 76D55 / 76A05
Key words: Optimal control / multistate Navier-Stokes equations / shear-dependent viscosity / necessary optimality conditions
© EDP Sciences, SMAI, 2012