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On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces. (English) Zbl 1194.35322

Summary: This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. If the velocity field satisfies \(u \in L^{\frac {2}{1+r}} (0,T;B^r_{\infty,\infty}(\mathbb R^3))\) 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:

35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
35D30 Weak solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
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