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Regularity of the adjoint state for the instationary Navier-Stokes equations

Rösch, Arnd; Wachsmuth, Daniel

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

In 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.