Global Well-Posedness for the Fractional Navier-Stokes-Coriolis Equations in Function Spaces Characterized by Semigroups

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.