Improvement of several regularity criteria for the Navier–Stokes equations. (June 2022)

• Record Type: Journal Article
• Authors: Wu, Fan
• Is Part Of: Nonlinear analysis. Volume 65(2022)
• Publication Date: 2022-06
• Subjects: Navier–Stokes equations -- Conditional regularity -- Mixed-norm Lebesgue space -- Sum space; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103464
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider the incompressible Navier–Stokes equations (NSE) in the entire three-dimensional space. Assuming additional regularity on the components of the vector field u, or direction of the velocity u | u |, we show two regularity results in the mixed-norm Lebesgue sum spaces and improve, in some sense, previous results by Miller, Vasseur and Montgomery-Smith.