Preprint 12-2010

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

Author(s) : Etienne Emmrich , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 12-2010

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34G10 Linear equations

Abstract :
Existence and uniqueness of solutions to initial value problems for a class of abstract differential-algebraic equations (DAEs) is shown. The class of equations cover, in particular, the spatially semi-discretized Stokes and Oseen problem describing the motion of an incompressible or nearly incompressible Newtonian fluid. Moreover, we derive explicit solution formulas.

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