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

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

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 inv...

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Veröffentlicht in:Zeitschrift für Analysis und ihre Anwendungen 2005-01, Vol.24 (1), p.103-116
Hauptverfasser: Rösch, Arnd, Wachsmuth, Daniel
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Sprache:eng
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Fourier analysis
Functional analysis
Potential theory
Real functions
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container_title Zeitschrift für Analysis und ihre Anwendungen
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Wachsmuth, Daniel
description 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.
doi_str_mv 10.4171/ZAA/1231
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subjects Fourier analysis
Functional analysis
Potential theory
Real functions
title Regularity of the Adjoint State for the Instationary Navier-Stokes Equations
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