Regularity for 3D Navier-Stokes Equations Based on Energy Distribution at Wavenumber Bands

We present some regularity criteria for the Leray-Hopf weak solutions to the Cauchy problem for 3D Navier-Stokes equations based on energy distribution at wavenumber bands. We show sufficient conditions for regularity based on the ratios of energy dissipation rates at sufficiently high wavenumber bands and neighboring medium wavenumber bands. Moreover, we give a regularity criterion based on relations between energy at high and low wavenumber bands.