In this paper, we consider the bidimensional exterior unsteady Navier-Stoke
s equations with nonhomogeneous boundary conditions and present an Oseen co
upling problem which approximates the Navier-Stokes problem, obtained by co
upling the Navier-Stokes equations in the inner region and the Oseen equati
ons in the outer region. Moreover, we prove the existence, uniqueness and t
he approximate accuracy of the weak solution of the Oseen coupling equation
s.