Remarks on the Possible Blow-Up Conditions via One Velocity Component for the 3D Navier–Stokes Equations

Remarks on the Possible Blow-Up Conditions via One Velocity Component for the 3D Navier–Stokes Equations

In this paper, we study some blow-up conditions via one velocity component for the 3D incompressible Navier–Stokes equations in the framework of scaling invariant anisotropic Besov spaces. In particular, we prove that if one component of the velocity remains small enough in the space H ˙ 1 2 , then...

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Veröffentlicht in:The Journal of geometric analysis 2024-06, Vol.34 (6), Article 170
Hauptverfasser: Guo, Zhengguang, O, Chol-Jun
Format: Artikel
Sprache:eng
Schlagworte:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fluid flow
Fourier Analysis
Function space
Global Analysis and Analysis on Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Navier-Stokes equations
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Zusammenfassung:In this paper, we study some blow-up conditions via one velocity component for the 3D incompressible Navier–Stokes equations in the framework of scaling invariant anisotropic Besov spaces. In particular, we prove that if one component of the velocity remains small enough in the space H ˙ 1 2 , then there is no blow-up. This result improves the previous ones by Chemin et al. (Commun Partial Differ Equ 44:1387-1405, 2019) and Houamed (J Differ Equ 275:116–138, 2021).
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01613-w