A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion. (February 2015)

• Record Type: Journal Article
• Authors: Zhang, Lei; Li, Shan
• Is Part Of: Nonlinear analysis. Volume 21(2015)
• Page Start: 197
• Page End: 206
• Publication Date: 2015-02
• Subjects: Regularity criterion -- 2D MHD system -- Classical solution -- Horizontal dissipation and magnetic diffusion; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.07.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper concerns the conditional global regularity of incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion in two dimension. When only horizontal dissipation and horizontal magnetic diffusion are present, there is no control on the vertical derivatives of velocity field and magnetic field, which is the main difficulty to establish the global regularity. In this paper, we establish a global regularity criterion in terms of one entry of the velocity gradient tensor or one entry of the magnetic field gradient tensor, which extends the recent work (Fan and Ozawa, 2014).