Nadir Arada

This paper is concerned with steady, fully developed motion of a Navier--Stokes fluid with shear-dependent viscosity in a curved pipe under a given axial pressure gradient. We establish existence and uniqueness results, derive appropriate estimates, and prove a characterization of the secondary flows. The approximation, with respect to the curvature ratio, of the full governing systems by some Dean-like equation is studied.

We are interested in the necessary optimality conditions for optimal control problems of systems describing the unsteady flow of incompressible shear-thickening fluids. To overcome the difficulties related to the differentiability of the control-to-state mapping, consequence of the lack of regularity of the state variable, we first establish some intermediate optimality conditions and then pass to the limit.

We study optimal control problems of systems describing the flow of incompressible shear-thickening fluids. We prove existence of solutions and derive necessary optimality conditions under precise restrictions on the optimal control.

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.