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Zeitschrift für Analysis und ihre Anwendungen

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Volume 24, Issue 1, 2005, pp. 103–116
DOI: 10.4171/ZAA/1231

Published online: 2005-03-31

Regularity of the Adjoint State for the Instationary Navier-Stokes Equations

Arnd Rösch[1] and Daniel Wachsmuth[2]

(1) Universität Duisburg-Essen, Germany
(2) Technische Universität Berlin, Germany

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.

Keywords: Vector-valued functions, imbeddings, Navier-Stokes equations, optimal control, regularity of adjoints

Rösch Arnd, Wachsmuth Daniel: Regularity of the Adjoint State for the Instationary Navier-Stokes Equations. Z. Anal. Anwend. 24 (2005), 103-116. doi: 10.4171/ZAA/1231