Global solvability of the navier-stokes equations in spaces based on sum-closed frequency sets

We prove existence of global regular solutions for the 3D Navier-Stokes equations with (or without) Coriolis force for a class of initial data u₀ in the space FM_σ,δ, i.e., for functions whose Fourier image û₀ is a vector-valued Radon measure and that are supported in sumclosed frequency sets with distance δ from the origin. In our main result we establish an upper bound for admissible initial data in terms of the Reynolds number, uniform on the Coriolis parameter ω. In particular this means that this upper bound is linearly growing in δ. This implies that we obtain global-in-time regular solutions for large (in norm) initial data u₀ which may not decay at space infinity, provided that the distance δ of the sum-closed frequency set from the origin is sufficiently large.