Regularity results on the Leray-alpha magnetohydrodynamics systems. (December 2016)

• Record Type: Journal Article
• Authors: KC, Durga; Yamazaki, Kazuo
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 178
• Page End: 197
• Publication Date: 2016-12
• Subjects: Magnetohydrodynamics system -- Navier–Stokes equations -- Regularity -- Besov spaces; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.04.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in Zhou and Fan (2011). Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in Fan and Ozawa (2009).