Large time behavior of energy in exponentially decreasing solutions of the Navier–Stokes equations

We study large time behavior of exponentially decreasing global strong solutions of the Navier–Stokes equations. We show, as the main result, that these solutions are characterized by the asymptotic disappearance of low and high frequencies and concentration of energy in middle frequencies. We also describe a relationship between the spectrum of the Stokes operator and the class of exponentially decreasing global strong solutions.