2006/11/10 by Yueheng Lan, Lan, Yueheng, Y. Charles Li +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.nlin/0611021
53 pages, 39 figures
arxiv created 2006/11/10 · openalex publication_date 2006/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a rather comprehensive study on the dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes operator, (b). heteroclinics conjecture for Euler equation, its numerical verification, Melnikov integral, and simulation and control of chaos. Besides Navier-Stokes and Euler equations, we also study two models of them.