Regularity criterion for weak solutions to the 3D Navier–Stokes equations via two vorticity components in BMO−1. (June 2021)

• Record Type: Journal Article
• Authors: O, Chol-Jun
• Is Part Of: Nonlinear analysis. Volume 59(2021)
• Publication Date: 2021-06
• Subjects: Navier–Stokes equations -- Regularity criterion -- Vorticity -- Bony decomposition -- Besov spaces -- Triebel–Lizorkin spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103271
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we provide a regularity criterion for 3D Navier–Stokes equations in terms of two vorticity components, which extends a recent result established by Guo, Kučera and Skalák (2018). More precisely, we prove that a unique local strong solution u to 3D Navier–Stokes equations does not blow up at time T provided only two components of vorticity belongs to L 2 ( 0, T ; B M O − 1 ) . We also prove that u can be smoothly extended beyond T, if the horizontal gradient of horizontal components of velocity u belong to L 2 ( 0, T ; B M O − 1 ) . The proof relies on the technique of the Bony decomposition and some Fourier multiplier theorems.