A Stokes approximation of two dimensional exterior Oseen flow near the boundary

Abstract

In this paper, we are concerned with the linearized problems of the stationary Navier-Stokes equations for viscous incompressible fluids in two dimensional exterior domain. Obtained is an error estimate between solutions of the Oseen equations and the Stokes equations near the boundary. Our main theorem implies that Stokes's linearization still works well even in a two dimensional exterior domain if we consider the neighbourhoods of the boundary. In order to prove such estimate, we mainly use classical hydrodynamic potential theory.