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A new blow up criterion for the 3D magneto-micropolar fluid flows without magnetic diffusion
  • Dongxiang Chen,
  • Qifeng Liu,
  • Xiaoli Chen
Dongxiang Chen
Jiangxi Normal University

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Qifeng Liu
Jiangxi Normal University Yaohu Campus
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Xiaoli Chen
Jiangxi Normal University
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Abstract

This note obtains a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of one velocity component and the gradient field of the magnetic field, i.e. the weak solution $(u,\omega,b)$ to the magneto-micropolar fluid flows can be extended beyond time $t=T$, provided if $u_3\in L^{\beta}(0,T;L^{\alpha}({\R}^3))$ with $\f2{\beta}+\f3{\alpha}\leq\f34+\f1{2\alpha},\alpha>\f{10}3$ and $\nabla b\in L^\f{4p}{3(p-2)}(0,T;\dot{M}_{p,q}({\R}^3))$ with $1