no. 2
Optimal control of linearized compressible Navier-Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 587-615.

We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier-Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier-Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over the control set. Finally we derive an optimality system from which the optimal solution can be determined.

DOI : 10.1051/cocv/2012023
Classification : 49J20, 49K20, 35Q30, 76N25
Mots clés : optimal control, linearized compressible Navier-Stokes equations, boundary control, optimality system 
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     title = {Optimal control of linearized compressible {Navier-Stokes} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {587--615},
     publisher = {EDP-Sciences},
     volume = {19},
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     year = {2013},
     doi = {10.1051/cocv/2012023},
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Chowdhury, Shirshendu; Ramaswamy, Mythily. Optimal control of linearized compressible Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 2, pp. 587-615. doi : 10.1051/cocv/2012023. http://archive.numdam.org/articles/10.1051/cocv/2012023/

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