Global regularity of 3D rotating Navier-Stokes equations for resonant domains

We prove existence on infinite time intervals of regular solutions to the 3 D rotating Navier-Stokes equations in the limit of strong rotation (large C oriolis parameter Omega). This uniform existence is proven for periodic or stress-free boundary conditions for ail domain aspect ratios; including the case of three wave resonances which yield nonlinear " 21/2-dimensional" li mit equations; smoothness assumptions are the same as for local existence t heorems; The global existence is proven using techniques of the Littlewood- Paley dyadic decomposition. Infinite time regularity for solutions of the 3 D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems. (C) 2000 Elsev ier Science Ltd. All rights reserved.