no. 1
Distributed control for multistate modified Navier-Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 219-238

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.

DOI : 10.1051/cocv/2012007
Classification : 49K20, 76D55, 76A05
Keywords: optimal control, multistate Navier-Stokes equations, shear-dependent viscosity, necessary optimality conditions 
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     author = {Arada, Nadir},
     title = {Distributed control for multistate modified {Navier-Stokes} equations},
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     pages = {219--238},
     year = {2013},
     publisher = {EDP Sciences},
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     number = {1},
     doi = {10.1051/cocv/2012007},
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     url = {https://www.numdam.org/articles/10.1051/cocv/2012007/}
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Arada, Nadir. Distributed control for multistate modified Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 219-238. doi: 10.1051/cocv/2012007

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