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