Geodesic
Optimal Boundary Control of Steady-State Flow of a Viscous Inhomogeneous Incompressible Fluid
Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 666-678

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We study the problem of optimal boundary control of two-dimensional steady-state flow of a viscous inhomogeneous incompressible fluid. The role of control is played by the values of the velocity on a part of the boundary of the domain considered. On the remaining part of the boundary, the vector of flow velocity and the fluid density are given. We seek the fluid density as a scalar function (determined by the initial data) of the stream function, study the solvability of the problem, and obtain necessary optimality conditions. 
@article{MZM_2001_69_5_a2,
     author = {A. A. Illarionov},
     title = {Optimal {Boundary} {Control} of {Steady-State} {Flow} of a {Viscous} {Inhomogeneous} {Incompressible} {Fluid}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {666--678},
     publisher = {mathdoc},
     volume = {69},
     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a2/}
}
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A. A. Illarionov. Optimal Boundary Control of Steady-State Flow of a Viscous Inhomogeneous Incompressible Fluid. Matematičeskie zametki, Tome 69 (2001) no. 5, pp. 666-678. http://geodesic.mathdoc.fr/item/MZM_2001_69_5_a2/