Problem with the Derivation of the Navier-Stokes Equation by Means of Zwanzig-Mori Projection Technique of Statistical Mechanics

TL;DR

This paper critiques the derivation of the Navier-Stokes equation via the Zwanzig-Mori projection method, revealing that the resulting friction term's nonlinear component is incorrectly derived, leading to an inaccurate formula.

Contribution

It demonstrates that the second-order nonlinear term in the friction component, derived using multilinear mode-coupling, is non-zero, challenging previous derivations.

Findings

The second-order friction term is non-zero.

The standard derivation yields an incorrect formula.

The Zwanzig-Mori projection technique may be flawed for this derivation.

Abstract

The derivation of the Navier-Stokes equation starting from the Liouville equation using projection techniques yields a friction term which is nonlinear in the velocity. Using the results of multilinear mode-coupling technique for calculating equlibrium correlation functions, it is shown that the second-order part of the term is non-zero, thus leading to an incorrect formula for the equation.