The 3D nematic liquid crystal equations with blow-up criteria in terms of pressure

In this paper, we concern the 3D nematic liquid crystal equations and prove three almost Serrin-type blow-up criteria for the breakdown of local in time smooth solutions in terms of pressure and gradient of the orientation field. More precisely, let T-*, be the maximal time of the local smooth solution, then T-* < +infinity if and only if integral(T*)(0) parallel to parallel to parallel to P(center dot, t)parallel to(Lx1p) parallel to(Lx2q) parallel to(beta)(Lx3r) + parallel to del d(center dot, t)parallel to(8)(L4) dt = infinity, with 2/beta + 1/p + 1/q + 1/r = 2 and 2 <= p, q, r <= infinity,1 - (1/p + 1/q + 1/r) >= 0, and integral(T*)(0) parallel to parallel to parallel to del P(center dot, t)parallel to(Lx1p) parallel to(Lx2q) parallel to(beta)(Lx3r) + parallel to del d(center dot, t)parallel to(8)(L4) dt = infinity, with 2/beta + 1/p + 1/q + 1/r = 3 and 1 <= p, q, r <= infinity, 1 - (1/2p + 1/2q + 1/2r) >= 0, and integral(T*)(0) parallel to parallel to partial derivative P-3(center dot, t)parallel to(Lx3 gamma) parallel to(beta)(Lx1 x2 alpha) + parallel to del d(center dot, t)parallel to(8)(L4) dt = infinity, with 2/beta + 1/gamma + 2/alpha = k is an element of[2,3) and 3/k <= gamma <= alpha < 1/k-2. (C) 2017 Published by Elsevier Ltd.