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Zbl 1194.35322
Dong, Bo-Qing; Zhang, Wenliang
On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 7, 2334-2341 (2010). ISSN 0362-546X

Summary: This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. If the velocity field satisfies $u \in L^{\frac {2}{1+r}} (0,T;B^r_{\infty,\infty}(\Bbb R^3))$ for $-1<r<1$, then the weak solution $(u,w)$ is regular on $(0,T]$. The methods are mainly based on the Fourier localization technique and Bony's para-product decomposition.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
76W05 Flows in presence of electromagnetic forces
35D30
35B65 Smoothness of solutions of PDE

Keywords: micropolar fluid flows; regularity criterion; Besov spaces

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