Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 188, pp. 1-7.
Title: Blow-up criterion for strong solutions to the 3D
magneto-micropolar fluid equations in the multiplier space
Authors: Hui Zhang (Xiangtan Univ., Xiangtan, China)
Yongye Zhao (South China Univ. of Technology, Guangzhou, China)
Abstract:
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.