Tröltzsch, FrediWachsmuth, Daniel2021-12-172021-12-172003-09-182197-8085https://depositonce.tu-berlin.de/handle/11303/15489http://dx.doi.org/10.14279/depositonce-14262In this paper sufficient optimality conditions are established for optimal control of both steady-state and evolution 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 $L^\infty$.en510 Mathematikoptimal controlNavier-Stokes equationscontrol constraintssecond-order optimality conditionsfirst-order necessary conditionsResearch Paper