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 language | English |
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Pages (from-to) | 1517-1543 |
Number of pages | 27 |
Journal | Mathematische Annalen |
Volume | 389 |
Issue number | 2 |
Early online date | 20 Jul 2023 |
DOIs | |
Publication status | Published - 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.
Funders | Funder number |
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French National Research Agency | ANR-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