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Preprint 28-2013

Analysis of operator differential-algebraic equations arising in fluid dynamics. Part II. The infinite dimensional case

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Author(s) : Etienne Emmrich , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 28-2013

MSC 2000

34A09 Implicit equations, differential-algebraic equations
34G10 Linear equations

Abstract :
Existence and uniqueness of generalized solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations covers, in particular, the Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid but also their spatial semi-discretization. The equations are governed by a block operator matrix with entries that fulfill suitable inf-sup conditions. The problem data are required to satisfy appropriate consistency conditions. The results in infinite dimensions are compared in detail with those known for the DAEs that arise after semi-discretization in space. Explicit solution formulas are derived in both cases.

Keywords : Differential-algebraic equation, strangeness-index, existence, uniqueness, consistency, Duhamel's principle, Stokes equation, Oseen equation

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