Regularity criteria for liquid crystal system involving one derivative component of pressure. Issue 2 (22nd January 2022) - Zhao, Lingling; Li, Fengquan
Abstract : This paper is devoted to investigating regularity criteria for the nematic liquid crystal system in terms of one derivative component of the pressure and gradient of the orientation field. More precisely, we mainly proved that the strong solution ( u, d ) can be extended beyond T, provided that one derivative component of the pressure ∂ x 3 P and gradient of the orientation field satisfy 1 ∂ x 3 P ∈ L s ( 0, T ; L q ( R 3 ) ), 2 s + 3 q < 29 10, 30 23 < q ≤ 10 3, ∂ x 3 d ∈ L γ ( 0, T ; L β ( R 3 ) ), 2 γ + 3 β < 19 20, 60 13 < β ≤ 20 3 and 2 ∇ h d ∈ L γ 1 ( 0, T ; L β 1 ( R 3 ) ), 2 γ 1 + 3 β 1 ≤ 3 4 + 1 2 β 1, 60 13 < β 1 ≤ 20 3 .