Asymptotic behavior of the energy and pointwise estimates for solutions to the Navier-Stokes equations

Abstract

We study the large time behavior of the energy of a class of Navier-Stokes flows in ${\mathbb{R}}^n$ $(n\ge 2)$ with special symmetries. Inside this class, we construct examples of solutions such that the energy norm decays faster than $t^{-(n+2)/4}$.