ON THE ASYMPTOTIC DECAY OF HIGHER-ORDER NORMS OF THE SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN R3

Let A be the Stokes operator. We show as the main result of the paper that if w is a global weak solution to the Navier-Stokes equations satisfying the strong energy inequality, beta is an element of [0, 1/2] and alpha is an element of [beta, infinity), then there exist t(0) >= 1, C-1 > 1 and delta(1) is an element of (0, 1) such that parallel to A(alpha)w(t)parallel to <= C-1 parallel to A(beta) w(t+delta)parallel to for every t >= t(0) and every delta is an element of [0, delta(1)].