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

Tobias Barker, Pedro Gabriel Fernández-Dalgo, Christophe Prange

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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 (Arch Ration Mech Anal 214(2):525–544, 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.

Original languageEnglish
Pages (from-to)1517-1543
Number of pages27
JournalMathematische Annalen
Volume389
Issue number2
Early online date20 Jul 2023
DOIs
Publication statusPublished - 30 Jun 2024

Data Availability Statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Funding

CP and PFD are partially supported by the Agence Nationale de la Recherche, project BORDS, grant ANR-16-CE40-0027-01. CP is also partially supported by the Agence Nationale de la Recherche, project SINGFLOWS, grant ANR- 18-CE40-0027-01, project CRISIS, grant ANR-20-CE40-0020-01, by the CY Initiative of Excellence, project CYNA (CY Nonlinear Analysis) and project CYFI (CYngular Fluids and Interfaces). PFD is also supported by the Labex MME-DII. TB and CP thank the Institute of Advanced Studies of Cergy Paris University for their hospitality.

FundersFunder number
French National Research AgencyANR-20-CE40-0020-01, ANR- 18-CE40-0027-01, ANR-16-CE40-0027-01
French National Research Agency
Labex

    Keywords

    • 35A99
    • 35B44
    • 35B65
    • 35Q30
    • 76D05

    ASJC Scopus subject areas

    • General Mathematics

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