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

TL;DR

This paper introduces a new upper bound on the determining wavenumber for weak solutions of 3D Navier-Stokes equations, improving previous bounds by accounting for intermittency dimensions.

Contribution

It provides a refined upper bound on the determining wavenumber that applies across all intermittency dimensions, advancing understanding of turbulence modeling.

Findings

Improved upper bound on the determining wavenumber.

Applicable to all intermittency dimensions.

Enhances previous theoretical results.

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.