Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

Institut für Mathematik, Technische Universität Berlin, Str. d. 17. Juni 136, 10632 Berlin, Germany; troeltz@math.tu-berlin.de; wachsmut@math.tu-berlin.de

Received: 30 April 2004
Revised: 13 December 2004

Abstract

In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a L^s-neighborhood, whereby the underlying analysis allows to use weaker norms than L^∞.