Inertial manifolds for the incompressible Navier-Stokes equations

2019/10/14 by Xinhua Li, Chunyou Sun, Li, Xinhua +1
Computer Science · Engineering · Mathematics · #35B33 #35B40 #35B42 #35Q30 #76F20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.05939

openalex publication_date 2019/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we devote to the existence of an N-dimensional inertial manifold for the incompressible Navier-Stokes equations in \mathbbT^d (d=2,3). Our results can be summarized as two aspects: Firstly, we construct an N-dimensional inertial manifold for the Navier-Stokes equations in \mathbbT²; Secondly, we extend slightly the spatial averaging method to the abstract case: ∂_tu+A^1+αu+A^αF(u)=f (here 00 is a self-adjoint operator with compact inverse and F is Lipschitz from a Hilbert space ℍ to ℍ), and then verify the existence of an N-dimensional inertial manifold for the hyperviscous Navier-Stokes equation with the hyperviscous index 5/4 in \mathbbT³.

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