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

by M. Feistauer and Ch. Schwab

(Report number 1998-01)

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.

@Techreport{FS98_226,
  author = {M. Feistauer and Ch. Schwab},
  title = {Coupling of an Interior Navier-Stokes Problem with an Exterior Oseen Problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1998-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1998/1998-01.pdf },
  year = {1998}
}

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