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.
Mots clés : optimal control, linearized compressible Navier-Stokes equations, boundary control, optimality system
@article{COCV_2013__19_2_587_0, author = {Chowdhury, Shirshendu and Ramaswamy, Mythily}, 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}, number = {2}, year = {2013}, doi = {10.1051/cocv/2012023}, mrnumber = {3049725}, zbl = {1266.49006}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2012023/} }
TY - JOUR AU - Chowdhury, Shirshendu AU - Ramaswamy, Mythily TI - Optimal control of linearized compressible Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 587 EP - 615 VL - 19 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012023/ DO - 10.1051/cocv/2012023 LA - en ID - COCV_2013__19_2_587_0 ER -
%0 Journal Article %A Chowdhury, Shirshendu %A Ramaswamy, Mythily %T Optimal control of linearized compressible Navier-Stokes equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 587-615 %V 19 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012023/ %R 10.1051/cocv/2012023 %G en %F COCV_2013__19_2_587_0
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://www.numdam.org/articles/10.1051/cocv/2012023/
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