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

For arbitrary domain $\Omega\subset\mathbb R^n$, $n=2,3$, $\Omega\ne\mathbb R^2$, 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 show also that the periodic regular solutions are stable. Bibl. 38 titles.