The aim of this study was to establish a new regularity criterion for local-in-time smooth solutions for the 3D nematic liquid crystal flows in terms of the horizontal gradient of two horizontal velocity components in the framework of the homogeneous Besov [Formula: see text] space and one directional derivative of molecular orientations in the framework of the homogeneous Morrey–Campanato [Formula: see text] space. More precisely, we show that the smooth solution [Formula: see text] can be extended beyond [Formula: see text], provided that [Formula: see text]
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Omrane et al. (2024) studied this question.
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