Regularity criteria for the Navier–Stokes equations based on one component of velocity. (June 2017)

• Record Type: Journal Article
• Authors: Guo, Zhengguang; Caggio, Matteo; Skalák, Zdeněk
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 379
• Page End: 396
• Publication Date: 2017-06
• Subjects: Navier–Stokes equations -- Regularity of solutions -- Regularity criteria -- Anisotropic Lebesgue spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.11.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study the regularity criteria for the incompressible Navier–Stokes equations in the whole space R 3 based on one velocity component, namely u 3, ∇ u 3 and ∇ 2 u 3 . We use a generalization of the Troisi inequality and anisotropic Lebesgue spaces and prove, for example, that the condition ∇ u 3 ∈ L β ( 0, T ; L p ), where 2 / β + 3 / p = 7 / 4 + 1 / ( 2 p ) and p ∈ ( 2, ∞ ], yields the regularity of u on ( 0, T ] .