Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations

In this paper we study the space-time asymptotic behavior of the solutions, and their derivatives, to the incompressible Navier Stokes equations in di mension 2 less than or equal to n less than or equal to 5. Using moment est imates we obtain that strong solutions to the Navier Stokes equations which decay in L-2 at the rate of parallel to u(t)parallel to(2) less than or eq ual to C (t + 1)(-mu) will have the following pointwise space-time decay, f or 0 less than or equal to k less than or equal to n/2: \D(alpha)u(x,t)\ less than or equal to C-k,C-m 1/(t + 1)(rho 0) (1 + \x\(2) )(k/2), where rho(O) = (1 = 2k/n)(m/2+ mu + n/4), \alpha\ = m and mu > n/4.