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

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.