Report 1998-01

Coupling of an Interior Navier--Stokes Problem with an Exterior Oseen Problem

M. Feistauer and C. Schwab

Abstract: The paper is concerned with the modelling of viscous incompressible flow in an unbounded exterior domain with the aid of the coupling of the nonlinear Navier--Stokes equations considered in a bounded domain with the linear Oseen system in an exterior domain. These systems are coupled on an artificial interface via suitable transmission conditions. The present paper is a continuation of the work [8], where the coupling of the Navier--Stokes problem with the Stokes problem is treated. However, the coupling "Navier--Stokes -- Oseen" is physically more relevant. We give the formulation of this coupled problem and prove the existence of its weak solution for large data.

Keywords: viscous incompressible flow, Navier--Stokesequations, exterior Oseen problem, transmission conditions, coupledproblem, weak solution.

Paper: Available as PDF (289 KB) or as hardcopy to order reports@sam.math.ethz.ch.