Dynamics of scaled norms of vorticity for the three-dimensional Navier-Stokes and Euler equations

摘要

A series of numerical experiments is suggested for the three-dimensional Navier-Stokes and Euler equations on a periodic domain based on a set of L~(2m)-norms of vorticity Ω_m for m ≥ 1. These are scaled to form the dimensionless sequence D_m = ((ω_0)~(-1)Ω_m)~(α_m) whereω_0 is a constant frequency and α_m = 2m/(4m - 3). A numerically testable Navier-Stokes regularity criterion comes from comparing the relative magnitudes of D_m and D_(m+1) while another is furnished by imposing a critical lower bound on ∫D_m dτ(0<τ