Wachsmuth, Daniel2021-12-172021-12-172004-05-012197-8085https://depositonce.tu-berlin.de/handle/11303/15540http://dx.doi.org/10.14279/depositonce-14313The aim of this article is to present a convergence theory of the SQP-method applied to optimal control problems for the instationary Navier-Stokes equations. We will employ a second-order sufficient optimality condition, which requires that the second derivative of the Lagrangian is positive definit on a subspace of inactive constraints. Therefore, we have to use $L^p$-theory of optimal controls of the instationary Navier-Stokes equations rather than Hilbert space methods. We prove local convergence of the SQP-method. This behaviour is confirmed by numerical tests.en510 Mathematikoptimal controlNavier-Stokes equationscontrol constraintsLipschitz stabilitySQP-methodResearch Paper