  We consider the incompressible Navier-Stokes equations with the Dirichlet
boundary condition in an exterior domain of $\mathbb{R}^n$ with $n\geq2$. We
compare the long-time behaviour of solutions to this initial-boundary value
problem with the long-time behaviour of solutions of the analogous Cauchy
problem in the whole space $\mathbb{R}^n$. We find that the long-time
asymptotics of solutions to both problems coincide either in the case of small
initial data in the weak $L^{n}$-space or for a certain class of large initial
data.
