Fractional Navier-Stokes equations regularity criteria in terms of deformation tensor

We consider the singularity formation of strong solutions to the three-dimensional incompress-ible fractional Navier-Stokes equations in the whole space. By making use of the Bony decomposition technique, we prove that a unique local strong solution does not blow-up at time T if deformation tensor belongs to nonhomogeneous Besov spaces. As a bi-product, the result improves some well-known results on regularity for the particular case of classical Navier-Stokes equations.