# American Institute of Mathematical Sciences

December  2016, 9(6): 2167-2179. doi: 10.3934/dcdss.2016090

## Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space

 1 School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan 2 School of Mathematics and Information Science, Henan Polytechnic University, Henan 454000, China

Received  July 2015 Revised  September 2016 Published  November 2016

In this paper, we investigate the blow-up criteria of smooth solutions and the regularity of weak solutions to the micropolar fluid equations in three dimensions. We obtain that if $\nabla_{h}u,\nabla_{h}\omega\in L^{1}(0,T;\dot{B}^{0}_{\infty,\infty})$ or $\nabla_{h}u,\nabla_{h}\omega\in L^{\frac{8}{3}}(0,T;\dot{B}^{-1}_{\infty,\infty})$ then the solution $(u,\omega)$ can be extended smoothly beyond $t=T$.
Citation: Baoquan Yuan, Xiao Li. Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2167-2179. doi: 10.3934/dcdss.2016090
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