The paper deals with the construction of mild periodic solutions to the Navier–Stokes system in a family of domains close to the half space \(\mathbb {R}^n_+\) with boundary moving periodically in time and perturbed locally in space. In a preceding article the authors dealt with basic properties of the underlying modified Stokes operators, their adjoints and the construction of their evolution operators with estimates locally in time. The present paper proves via a decomposition into low and high frequency parts global estimates of the evolution operator with algebraic decay rates of order less than − 1. Then nonlinear estimates using also duality techniques show that a corresponding Poincaré map locally has a unique fixed point, the mild periodic solution. Various results also hold globally in time in the case that the compactly supported perturbation of \(\partial \mathbb {R}^n_+\) is uniformly bounded; they allow to construct mild solutions of the initial-boundary value problem.
