Electron. J. Diff. Equ., Vol. 2012 (2012), No. 188, pp. 1-7.

Blow-up criterion for strong solutions to the 3D magneto-micropolar fluid equations in the multiplier space

Hui Zhang, Yongye Zhao

In this article, we study the blow-up of strong solutions to the magneto-micropolar (MMP) fluid equations in $\mathbb{R}^3$. It is proved that if the gradient field of velocity satisfies
 \nabla u\in L^{2/(2-r)}(0,T;\dot{X}_r(\mathbb{R}^3))\quad
 \hbox{with }r\in[0,1],
then the strong solution $(u,w,b)$ can be extended beyond t=T.

Submitted March 30, 2012. Published October 28, 2012.
Math Subject Classifications: 35Q30, 76D05.
Key Words: Magneto-micropolar equations; blow-up criterion; multiplier spaces.

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Hui Zhang
School of Mathematical Science
Xiangtan University
Xiangtan 411105, China
email: zhangxtu@126.com
Yongye Zhao
Department of Mathematics
South China University of Technology
Guangzhou 510640, China
email: zhao.yongye@mail.scut.edu.cn

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