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

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

• Lipschitz
• stability
• optimal
• controls
• steady-state
• Navier-Stokes
• equations