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

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Abstract

We study the generalized magneto-hydrodynamics-\({\alpha}\) 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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Washington State University, Pullman, WA, 99164-3113, USA

    Kazuo Yamazaki

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  1. Kazuo Yamazaki
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Correspondence to Kazuo Yamazaki.

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Communicated by H. Kozono

K. Yamazaki expresses gratitude to Professor Jiahong Wu and Professor David Ullrich for their teaching, and the referee for helpful comments that improved the manuscript greatly.

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Yamazaki, K. A Remark on the Two-Dimensional Magneto-Hydrodynamics-Alpha System. J. Math. Fluid Mech. 18, 609–623 (2016). https://doi.org/10.1007/s00021-016-0259-4

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  • DOI: https://doi.org/10.1007/s00021-016-0259-4

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