JournalszaaVol. 24 , No. 1DOI 10.4171/zaa/1231

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

  • Arnd Rösch

    Universität Duisburg-Essen, Germany
  • Daniel Wachsmuth

    Technische Universität Berlin, Germany
Regularity of the Adjoint State for the Instationary Navier-Stokes Equations cover

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.