2014/01/24 by Kazuo Yamazaki, Yamazaki, Kazuo
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1401.6237
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
openalex publication_date 2014/01/24 · arxiv created 2016/03/18 · arxiv updated 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the two-dimensional generalized magnetohydrodynamics-α 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.