Regularity and Stability of optimal controls of instationary Navier-Stokes equations

Abstract

The regularity and stability of optimal controls of instationary Navier-Stokes equations is 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.