Volume 19, Number 2, April-June 2013
|Page(s)||587 - 615|
|Published online||21 February 2013|
Optimal control of linearized compressible Navier–Stokes equations
Received: 9 December 2011
Revised: 21 April 2012
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.
Mathematics Subject Classification: 49J20 / 49K20 / 35Q30 / 76N25
Key words: Optimal control / linearized compressible Navier–Stokes equations / boundary control / optimality system
© EDP Sciences, SMAI, 2013
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