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

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