Regularity criteria for the 3D MHD equations involving one current density and the gradient of one velocity component. (March 2015)

• Record Type: Journal Article
• Authors: Zhang, Zujin
• Is Part Of: Nonlinear analysis. Volume 115(2015)
• Page Start: 41
• Page End: 49
• Publication Date: 2015-03
• Subjects: 35B65 -- 35Q35 -- 76D03; MHD equations -- Navier–Stokes equations -- Regularity criteria -- Regularity of solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.12.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the Cauchy problem for the 3 D MHD equations, and provide a regularity criterion involving ∇ u 3 and j 3, where u 3 and j 3 are the third component of the velocity and the current density, respectively. As by-products, we show that assumptions on two vorticity and one current density component are enough to ensure the smoothness of the solution, and improve some previous results (Skalak, 2014; Zhou and Pokorný, 2009, 2010) for the Navier–Stokes equations.