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Optimal control of linearized compressible Navier–Stokes equations

Published online by Cambridge University Press:  21 February 2013

Shirshendu Chowdhury  and
Mythily Ramaswamy
Shirshendu Chowdhury
Affiliation:
T.I.F.R Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Office, 560065 Bangalore, India. shirshendu@math.tifrbng.res.in; mythily@math.tifrbng.res.in
Mythily Ramaswamy
Affiliation:
T.I.F.R Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Office, 560065 Bangalore, India. shirshendu@math.tifrbng.res.in; mythily@math.tifrbng.res.in
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Abstract

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.

Keywords

Optimal controllinearized compressible Navier–Stokes equationsboundary controloptimality system

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 587 - 615
Copyright
© EDP Sciences, SMAI, 2013

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