Two Logarithmically Improved Regularity Criteria for the 3D Nematic Liquid Crystal Flows. (22nd December 2022) - Wang, Ruirui; Mu, Qiang; Wang, Yulei; Li, Qiang
Abstract : In this paper, we study the regularity criterion for the local smooth solution of the 3D nematic liquid crystal flows. More precisely, it is proved the smooth solution u, d can be extended beyond T provided that ∫ 0 T ∇ h u h B ˙ ∞, ∞ 0 + ∇ d B ˙ ∞, ∞ 0 2 / 1 + log 1 + ∇ u B ˙ ∞, ∞ 0 + ∇ d B ˙ ∞, ∞ 0 d t < ∞ or ∫ 0 T ∇ h u h B ˙ ∞, ∞ − r 4 / 3 − 2 r + ∇ d B ˙ ∞, ∞ 0 2 / 1 + log 1 + ∇ u B ˙ ∞, ∞ 0 + ∇ d B ˙ ∞, ∞ 0 d t < ∞, 0 ≤ r ≤ 1 .