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

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.