New results on the constants in some inequalities for the Navier-Stokes quadratic nonlinearity

TL;DR

This paper provides explicit bounds for constants in inequalities related to the quadratic nonlinearity of the Navier-Stokes equations on a torus, extending previous work with more precise estimates.

Contribution

It offers fully explicit upper and lower bounds for key constants in inequalities for Navier-Stokes quadratic nonlinearity, improving understanding of these inequalities.

Findings

Explicit bounds for constants in Navier-Stokes inequalities

Extension of previous inequalities with Nash-Moser type generalizations

Enhanced precision in constants estimation

Abstract

We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier-Stokes equations on the torus T^d. These inequalities are "tame" generalizations (in the sense of Nash-Moser) of the ones analyzed in the previous works [Morosi and Pizzocchero: CPAA 2012, Appl.Math.Lett. 2013].