Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

Abstract

We establish a global existence result for the rotating Navier-Stokes equations with ondecaying initial data in a critical space which includes a large class of almost periodic unctions. The scaling invariant function space we introduce is given as the divergence of the pace of 3×3 fields of Fourier transformed finite Radon measures. The smallness condition n initial data for global existence is explicitly given in terms of the Reynolds number. The ondition is independent of the size of the angular velocity of rotation