Existence, uniqueness, and attainability of periodic solutions of the Navier-Stokes equations in exterior domains

For an arbitrary domain Ω ⊂ ℝn, n=2,3, Ω ≠ ℝn, we prove the existence of weak periodic solutions to the Navier-Stokes equations and of regular solutions if the data are small or satisfy certain symmetry conditions. We also show that the periodic regular solutions are stable. Bibliography: 38 titles.