JournalszaaVol. 24, No. 1pp. 103–116

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

  • Arnd Rösch

    Universität Duisburg-Essen, Germany

  • Daniel Wachsmuth

    Technische Universität Berlin, Germany
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Abstract

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.

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Arnd Rösch, Daniel Wachsmuth, Regularity of the Adjoint State for the Instationary Navier-Stokes Equations. Z. Anal. Anwend. 24 (2005), no. 1, pp. 103–116

DOI 10.4171/ZAA/1231