The end-point regularity criterion for the Navier–Stokes equations in terms of ∂3u. (October 2020)

• Record Type: Journal Article
• Authors: Skalak, Zdenek
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Navier–Stokes equations -- Optimal regularity criteria -- Anisotropic Lebesgue spaces -- Anisotropic version of Troisi inequality; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103120
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We show the following extension of the recent optimal regularity results by Kukavica & Ziane, Cao and Zhang: If u is a solution of the Navier–Stokes equations in the whole space R 3 and ∂ 3 u ∈ L p ( 0, T ; L q ( R 3 ) ), T > 0, where 2 ∕ p + 3 ∕ q = 2 and q ∈ ( 3 ∕ 2, 3 ], then u is regular on ( 0, T ] .