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 for strong rotation (large Coriolis para meter Omega). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of thr ee wave resonances which yield nonlinear "2 1/2- dimensional" limit equatio ns for Omega --> +infinity; smoothness assumptions are the same as for loca l existence theorems. The global existence is proven using techniques of th e Littlewood-Paley dyadic decomposition. Infinite time regularity for solut ions of the 3D rotating Navier-Stokes equations is obtained by bootstrappin g from global regularity of the limit equations and convergence theorems. I n generic cases, sharper regularity results are derived from the algebraic geometry of resonant Poincare curves.