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We consider the incompressible Navier–Stokes equations with the Dirichlet boundary condition in an exterior domain of    R  n    with    n  ⩾  2   . 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    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.

Asymptotics of solutions to the Navier–Stokes system in exterior domains