Remarks on generalized NSE regularity criteria

We consider the Cauchy problem for the 3D generalized Navier–Stokes equations. By making use of the littlewood-paley decomposition and various interpolation inequalities, we will prove several regularity criteria in terms of homogeneous Vishik spaces that may be larger than the homogeneous Besov spaces. As a bi-product, the results improve some well-known results on regularity for the particular case of classical Navier–Stokes equations.