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Preprint 749-2002

Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations

Source file is available as :   Postscript Document

Author(s) : Tomas Roubicek , Fredi Tröltzsch

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 749-2002

MSC 2000

49J20 Optimal control problems involving partial differential equations
49K20 Problems involving partial differential equations
49K40 Sensitivity, stability, well-posedness
35Q30 Stokes and Navier-Stokes equations
76D55 Flow control and optimization
90C31 Sensitivity, stability, parametric optimization

Abstract :
An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.

Keywords : Incompressible viscous fluids, flow control, first- and second-order optimality conditions, Lipschitz stability

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