2000/05/03 by Jerrold E. Marsden, Marsden, Jerrold E., Steve Shkoller +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Nonlinear Waves and Solitons #math.AP #math.DG
paper · pdf · doi:10.48550/arxiv.math/0005033
24 pages, 1 figure
openalex publication_date 2000/05/03 · arxiv created 2000/05/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to derive the anisotropic averaged Euler equations and to study their geometric and analytic properties. These new equations involve the evolution of a mean velocity field and an advected symmetric tensor that captures the fluctuation effects. Besides the derivation of these equations, the new results in the paper are smoothness properties of the equations in material representation, which gives well-posedness of the equations, and the derivation of a corrector to the macroscopic velocity field. The numerical implementation and physical implications of this set of equations will be explored in other publications.