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 what sense the initial value problem for the adjoint equation can be solved.
Cite this article
Arnd Rösch, Daniel Wachsmuth, Regularity of the Adjoint State for the Instationary Navier-Stokes Equations. Z. Anal. Anwend. 24 (2005), no. 1, pp. 103–116DOI 10.4171/ZAA/1231