Abstract: | We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n?3. Our proof is based on Lp–Lq estimates of the Stokes semigroup. We apply Lp–Lq estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd. |