Global stability for the fractional Navier-Stokes equations in the Fourier-Herz space

We consider global stability for the fractional incompressible Navier-Stokes equations in a 3-D critical Fourier-Herz space. By introducing a weighted norm space and using Fourier localization technique, the stability of mild solutions with small initial F(R3) perturbation is established. With the Friedrichs method, the stability of weak solutions is proved under arbitrary large initial L2(R3) perturbation.