Global solutions to the rotating Navier-Stokes equations with large data in the critical Fourier-Besov spaces

We consider the initial value problem for the 3D incompressible Navier-Stokes equations with the Coriolis force. The aim of this paper is to prove the existence of a unique global solution with arbitrarily large initial data in the scaling critical Fourier-Besov spaces <((B) over dot)over cap>(3/p-1)(p,sigma) (R-3)(3) (2 <= p < 4, 1 <= sigma < infinity), provided that the size of the Coriolis parameter is sufficiently large. Moreover, if the initial data additionally belong to the scaling sub-critical spaces, we obtain an explicit relationship between the initial data and the Coriolis force, which ensures the existence of a unique global solution.