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Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure. (English) Zbl 1210.35189

Summary: We study the regularity criterion of weak solutions to the three-dimensional (3D) micropolar fluid flows. It is proved that if the pressure satisfies

$\pi \in {L}^{q}\left(0,T;{B}_{p,\infty }^{r}\left({ℝ}^{3}\right)\right),\phantom{\rule{1.em}{0ex}}\frac{2}{q}+\frac{3}{p}=2+r,\phantom{\rule{1.em}{0ex}}\frac{3}{2+r}

then the weak solution $\left(u,w\right)$ becomes a regular solution on $\left(0,T\right]$. The methods are based on the innovative function decomposition technique.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 35D30 Weak solutions of PDE 35B65 Smoothness and regularity of solutions of PDE
##### Keywords:
micropolar fluid flows; pressure criterion; Besov spaces
##### References:
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