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

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