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

Abstract

AbstractWe 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 (, ), 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.