Existence and Uniqueness Results for Problems Arising in Connection with theIncompressible Navier-Stokes Equations

摘要

Boundary value and coupling problems for a system of partial differentialequations obtained by applying the Rothe method to the incompressible Navier-Stokes equations are studied. Uniqueness theorems for the coupling and for the three fundamental boundary value problems in interior and exterior domains are obtained. Existence theorems are obtained by applying the first part of Fredholm's alternative to modified boundary integral equations obtained from an ansatz approach as well as from representation theorems. Corresponding boundary integral equations of the first kind are studied. Some formulae for the calulation of the drag are derived.