Regularity Conditions of 3D Navier-Stokes flow in terms of large spectral components

2014/05/27 by Namkwon Kim, Kim, Namkwon, Minkyu Kwak +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1405.6838

11 pages

arxiv created 2014/05/27 · openalex publication_date 2014/05/27 · arxiv updated 2014/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop Ladyzhenskaya-Prodi-Serrin type spectral regularity criteria for 3D incompressible Navier-Stokes equations in a torus. Concretely, for any N>0, let w_N be the sum of all spectral components of the velocity fields whose all three wave numbers are greater than N absolutely. Then, we show that for any N>0, the finiteness of the Serrin type norm of w_N implies the regularity of the flow. It implies that if the flow breaks down in a finite time, the energy of the velocity fields cascades down to the arbitrarily large spectral components of w_N and corresponding energy spectrum, in some sense, roughly decays slower than κ^-2

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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