Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in \R³

2023/11/30 by Yongqian Han, Han, Yongqian
Earth and Planetary Sciences · Mathematics · #35Q30 #37L20 #76D05 #76F02 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #FOS: Physical sciences #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2311.18308

openalex publication_date 2023/11/30 · openalex created_date 2023/12/02 · openalex updated_date 2026/07/28

Abstract

The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large enough and time variable t goes to infinity, these random solutions of static Euler equations are the path limits of corresponding Navier-Stokes flows. But the double limit of these Navier-Stokes flows do not exist. Therefore these solutions are called turbulent solutions.

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