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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
Article

Abstract

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.

Keywords

Regularity criteria Generalized MHD system Fractional diffusion 

Mathematics Subject Classification (2000)

35B65 35Q30 76D03 

Notes

Acknowledgements

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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