Abstract

This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. When the velocity field satisfies u ∈ L 2 1 + r ( 0 , T ; B ∞ , ∞ r ( 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.

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