Critical regularity criteria for Navier-Stokes equations in terms of one directional derivative of the velocity

2020/07/21 by Hui Chen, Chen, Hui, Daoyuan Fang +3 · 1 citation
Engineering · Mathematics · #A priori and a posteriori #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Combinatorics #Computer science #Derivative (finance) #Directional derivative #FOS: Mathematics #Field (mathematics) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Navier-Stokes equation solutions #Navier–Stokes equations #Physics #Pure mathematics #Space (punctuation) #Stability and Controllability of Differential Equations #Vector field #math.AP

paper · pdf · doi:10.48550/arxiv.2007.10888

published in arXiv (Cornell University) (Cornell University)

arxiv created 2020/07/21 · openalex publication_date 2020/07/21 · arxiv updated 2020/07/22 · openalex created_date 2020/07/29 · openalex updated_date 2026/08/05

Abstract

In this paper, we consider the 3D Navier-Stokes equations in the whole space. We investigate some new inequalities and a priori estimates to provide the critical regularity criteria in terms of one directional derivative of the velocity field, namely ∂₃ u ∈ L^p((0,T); L^q(ℝ³)), ~(2)/(p) + (3)/(q) = 2, ~(3)/(2)

Citations

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

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