Regularity criteria for the Navier–Stokes equations based on one or two items of the velocity gradient. (December 2017)

• Record Type: Journal Article
• Authors: Skalák, Zdeněk
• Is Part Of: Nonlinear analysis. Volume 38(2017)
• Page Start: 131
• Page End: 145
• Publication Date: 2017-12
• Subjects: Navier–Stokes equations -- Regularity criteria -- Troisi inequality -- Anisotropic Lebesgue spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.04.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the regularity criteria for the incompressible Navier–Stokes equations based on either one item of the velocity gradient, ∂ 1 u 3 or ∂ 3 u 3 or on two items of the velocity gradient, ∂ 2 u 3, ∂ 3 u 3, or ∂ 1 u 3, ∂ 2 u 3 . We improve and/or extend several results from the literature by the use of two versions of the generalized Troisi inequality.