A remark on the two-dimensional magneto-hydrodynamics-alpha system

Abstract

We study the two-dimensional generalized magnetohydrodynamics-$\alpha$ system with fractional Laplacians in the dissipative and diffusive terms. We show that the solution pair of velocity and magnetic fields preserves their initial regularity in all cases when the powers add up to one. This settles the global regularity issue in the general case which was remarked by the authors in [33] to be a problem.

The title has been modified, specifically, from "magnetohydrodynamics" to "magneto-hydrodynamics" for a editing reason during the publication process. To appear in J. Math. Fluid Mechanics

References in corpus (5)

• Analytical Study of Certain Magnetohydrodynamic-alpha Models
• A Remark On Global Regularity of 2D Generalized Magnetohydrodynamic Equations
• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
• Remarks on global regularity of 2D generalized MHD equations
• On the global regularity of two-dimensional generalized magnetohydrodynamics system