Exponential decay rate of the power spectrum for solutions of the Navier–Stokes equations

Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier–Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained.