The anisotropic regularity criteria for 3D Navier–Stokes equations involving one velocity component. (August 2020)

• Record Type: Journal Article
• Authors: Qian, Chenyin
• Is Part Of: Nonlinear analysis. Volume 54(2020)
• Publication Date: 2020-08
• Subjects: Navier–Stokes equations -- Leray–Hopf weak solution -- Anisotropic regularity criterion; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103094
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The anisotropic regularity criterion for the Navier–Stokes equations in terms of the one component of the velocity gradient ( ∂ i u j, 1 ≤ i, j ≤ 3 ) is investigated. It is an improvement of results of Qian (2016) and is also a complement of the results of Guo et al. (2018) for i = j . Besides, the consistent regularity criterion without distinguishing i = j and i ≠ j is also obtained. Finally, the regularity result based on the fractional derivatives for one component of the velocity field D h α u 3 with α ∈ [ 0, 1 ] is also established, which can be reduced to some previous results with α = 0 and α = 1 .