A Remark on the Two-Dimensional Magneto-Hydrodynamics-Alpha System

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We study the generalized magneto-hydrodynamics-α system in two dimensional space 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 Zhao and Zhu (Appl Math Lett 29:26–29, 2014) to be a problem.

Original languageEnglish
Pages (from-to)609-623
Number of pages15
JournalJournal of Mathematical Fluid Mechanics
Issue number3
StatePublished - Sep 1 2016


  • Magneto-hydrodynamics system
  • Navier–Stokes equations
  • fractional Laplacians
  • global regularity
  • α-regularization


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