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.
Categories: math.AP