# On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space

@inproceedings{Yuan2009OnRC,
title={On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space},
author={Baoquan Yuan},
year={2009}
}
In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space $L^{p,\infty}(\mathbb{R}^3)$. We obtain that if $u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 1$ with $3<p\le \infty$; or $\nabla u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 2$ with $\frac32<p\le \infty$; or the pressure $P\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for…
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