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On a shape control problem for the stationary Navier-Stokes equations

Published online by Cambridge University Press:  15 April 2002

Max D. Gunzburger ,
Hongchul Kim  and
Sandro Manservisi
Max D. Gunzburger
Affiliation:
Department of Mathematics, Iowa State University, Ames IA, 50011-2064, USA. (gunzburg@math.iastate.edu) Supported in part by the Air Force Office of Scientific Research under grant number F49620-95-1-0407.
Hongchul Kim
Affiliation:
Department of Mathematics, Kangnŭng National University, Kangnŭng 210-702, Korea. (hongchul@knusun.kangnung.ac.kr)
Sandro Manservisi
Affiliation:
Department of Mathematics, Kaiserslautern University, Kaiserslautern, 67663, Germany. Current address: LIN, DIENCA, University of Bologna, Via dei colli 16, 40136 Bologna, Italy. (sandro.manservisi@mail.ing.unibo.it) Supported by the European community under grant XCT-97-0117.
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Abstract

An optimal shape control problem for the stationary Navier-Stokes system is considered. An incompressible, viscous flow in a two-dimensional channel is studied to determine the shape of part of the boundary that minimizes the viscous drag. The adjoint method and the Lagrangian multiplier method are used to derive the optimality system for the shape gradient of the design functional.

Keywords

Shape controloptimal designNavier-Stokes equationsdrag minimization.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 6 , November 2000 , pp. 1233 - 1258
Copyright
© EDP Sciences, SMAI, 2000

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