Acta Applicandae Mathematicae

, Volume 149, Issue 1, pp 139–144 | Cite as

Generalized MHD System with Velocity Gradient in Besov Spaces of Negative Order

  • Zujin Zhang


This paper studies the 3D generalized MHD system with fractional diffusion terms \((-\triangle)^{\alpha}\boldsymbol{u}\) and \((-\triangle )^{\beta}\boldsymbol{b}\) with \(0<\alpha<\frac{5}{4}\leq\beta\), and establishes a regularity criterion involving the velocity gradient in Besov spaces of negative order. This improves Fan et al. (Math. Phys. Anal. Geom. 17:333–340, 2014) a lot.


Regularity criteria Generalized MHD system Fractional diffusion 

Mathematics Subject Classification (2000)

35B65 35Q30 76D03 



This work is supported by the National Natural Science Foundation of China (grants Nos. 11501125, 11361004).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.School of Mathematics and Computer SciencesGannan Normal UniversityGanzhouP.R. China

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