Rösch, ArndWachsmuth, Daniel2021-12-172021-12-172004-04-142197-8085https://depositonce.tu-berlin.de/handle/11303/15542http://dx.doi.org/10.14279/depositonce-14315In this article, we are considering imbeddings of abstract functions in spaces of functions being continuous in time. A family of functions depending on certain parameters is discussed in detail. In particular, this example shows that such functions do not belong to the space $C([0,T],H)$. In the second part, we investigate an optimal control problem for the instationary Navier-Stokes equation. We will answer the question, in which sense the initial value problem for the adjoint equation can be solved.en510 Mathematikvector-valued functionsimbeddingsoptimal controlNavier-Stokes equationsregularity of adjointsResearch Paper