Wachsmuth, Daniel2021-12-172021-12-172005-12-302197-8085https://depositonce.tu-berlin.de/handle/11303/15548http://dx.doi.org/10.14279/depositonce-14321We investigate optimal control problems with vector-valued controls. As model problem serve the optimal distributed control of the instationary Navier-Stokes equations. We study pointwise convex control constraints, which is a constraint of the form u(x,t)?U(x,t) that has to hold on the domain Q. Here, U is an set-valued mapping that is assumed to be measurable with convex and closed images. We establish first-order necessary as well as second-order sufficient optimality conditions. And we prove regularity results for locally optimal controls.en510 Mathematikoptimal controlconvex control constraintsset-valued mappingsactive-set strategyNavier-Stokes equationsResearch Paper