Blow-up of dynamically restricted critical norms near a potential Navier-Stokes singularity

2023/02/13 by Tobias Barker, Barker, Tobias, Pedro Gabriel Fernández-Dalgo +3
Engineering · Mathematics · #35A99 #35B44 #35B65 #35Q30 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.06509

openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/08/01

Abstract

In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the critical Lebesgue norm in general or the critical weak Lebesgue norm in the axisymmetric case. This type of results is inspired in particular by a work of Neustupa (2014), which handles certain non endpoint critical norms. Our work enables to have a better understanding of the nonlocal effect of the pressure on the regularity of the solutions.

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