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

2007/11/18 by J. Piest, Piest, J.
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Elasticity and Wave Propagation #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #General Physics (physics.gen-ph) #Geotechnical and Geomechanical Engineering #physics.class-ph #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.0711.2790

9 pages, no figures; prepared with Scientific Word

arxiv created 2007/11/18 · openalex publication_date 2007/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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