Global mild solution of the generalized Navier-Stokes equations with the Coriolis force

In this paper, we establish the global well-posedness of mild solution to the three-dimensional incompressible generalized Navier-Stokes equations with Coriolis force if the initial data are in X1−2α defined by X1−2α={u∈D′(R3):∫R3|ξ|1−2α|uˆ(ξ)|dξ<+∞}. In addition, we also give Gevrey class regularity of the solution.