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Regularity and stability of optimal controls of nonstationary Navier-Stokes equations

Wachsmuth D.

Control and Cybernetics

2005

Vol. 34, no 2

387-409

The regularity and stability of optimal controls of nonstationary Navier-Stokes equations are investigated. Under suitable assumptions every control satisfying first-order necessary conditions is shown to be a continuous function in both space and time. Moreover, the behaviour of a locally optimal control under certain perturbations of the cost functional and the state equation is investigated. Lipschitz stability is proven provided a second-order sufficient optimality condition holds.

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

Roubicek T., Troltzsch F.

Control and Cybernetics

2003

Vol. 32, no 3

683-705

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.