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Distributed control for multistate modified Navier-Stokes equations

Published online by Cambridge University Press:  02 May 2012

Nadir Arada
Nadir Arada*
Affiliation:
Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal. naar@fct.unl.pt
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Abstract

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.

Keywords

Optimal controlmultistate Navier-Stokes equationsshear-dependent viscositynecessary optimality conditions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 219 - 238
Copyright
© EDP Sciences, SMAI, 2012

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