1999/08/19 by Jerrold E. Marsden, J. E. Marsden, Marsden, J. E. +6 · 1 citation
Mathematics · Physics and Astronomy · #58B20 #58D05 #76E99 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Waves and Solitons #math.AP #math.DG #msc:58B20 #msc:58D05 #msc:76E99
paper · pdf · doi:10.48550/arxiv.math/9908103
arxiv created 1999/08/19 · openalex publication_date 1999/08/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of \mathbb Rn, this system of PDEs with Dirichlet boundary conditions are well-posed for initial data in the Hilbert space Hs, s>n/2+1. We then use a nonlinear Trotter product formula to prove that solutions of the averaged Euler equations are a regular limit of solutions to the averaged Navier-Stokes equations in the limit of zero viscosity. This system of PDEs is also the model for second-grade non-Newtonian fluids.