Author(s) :
Arnd Rösch
,
Daniel Wachsmuth
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 10-2004
MSC 2000
- 46E40 Spaces of vector- and operator-valued functions
-
49N60 Regularity of solutions
Abstract :
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.
Keywords :
Vector-valued functions, imbeddings, optimal control, Navier-Stokes equations, regularity of adjoints