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[0,T*)be the maximal time of the local smooth solution,then T*<+? if and only if?0T*???p(·,t)?Lx1p?Lx2q?Lx3r?+??d(·,t)?L48dt=?,with 2/?+1/p+1/q+1/r= 3 and 1 ? p,q,r ? ?,1-(1/2p + 1/2r)>0,and?0T*????p(·,t)?Lx1p?Lx2q?Lx3r?+??d(·,t)?L48dt=?,with 2/?+ 1/? +2/?=? ?[2,3)and 3/? ? ? ??<1/?-2.and?0T*??(?)3P(·,t)?Lx3??Lx1x2?? + ??d(·,t)?L48dt = ?,with 2/?+ 1/? +2/?=? ?[2,3)and 3/? ? ? ??<1/?-2.