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multistate navier-stokes equations

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Distributed control for multistate modified Navier-Stokesequations
Nadir Arada
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 1 / January 2013

Published online by Cambridge University Press:

02 May 2012, pp. 219-238

Print publication:

January 2013
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The aim of this paper is to establish necessary optimality conditions for optimal controlproblems governed by steady, incompressible Navier-Stokes equations with shear-dependentviscosity. The main difficulty derives from the fact that equations of this type mayexhibit non-uniqueness of weak solutions, and is overcome by introducing a family ofapproximate control problems governed by well posed generalized Stokes systems and bypassing to the limit in the corresponding optimality conditions.