2003/05/18 by Iliya V. Karlin, Larisa L. Tatarinova, Alexander N. Gorban +2
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fluid Dynamics and Turbulent Flows #Statistical Mechanics and Entropy #cond-mat.soft #cond-mat.stat-mech #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.1016/s0378-4371(03)00510-7
published as Physica A, Volume 327, Issues 3-4, 15 September 2003, Pages 399-424 · 32 pages, 2 figures, elsart, Physica A, to appear
arxiv created 2003/05/18 · openalex publication_date 2003/07/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recently introduced systematic approach to derivations of the macroscopic dynamics from the underlying microscopic equations of motions in the short-memory approximation [Gorban et al, Phys. Rev. E, 63, 066124 (2001)] is presented in detail. The essence of this method is a consistent implementation of Ehrenfest's idea of coarse-graining, realized via a matched expansion of both the microscopic and the macroscopic motions. Applications of this method to a derivation of the nonlinear Vlasov-Fokker-Planck equation, diffusion equation and hydrodynamic equations of the fluid with a long-range mean field interaction are presented in full detail. The advantage of the method is illustrated by the computation of the post-Navier-Stokes approximation of the hydrodynamics which is shown to be stable unlike the Burnett hydrodynamics.