An optimal upper bound on the determining wavenumber for 3D Navier-Stokes Equations

Abstract

We introduce a determining wavenumber for weak solutions of 3D Navier-Stokes equations whose time average is bounded by Kolmogorov dissipation wavenumber over the whole range of intermittency dimensions. This improves previous works by Cheskidov, Dai and Kavlie in 2018 and that by Cheskidov and Dai in 2019.

arXiv commentSeveral additional remarks on the time average determining wavenumber