On blow-up criteria for the 3D nematic liquid crystal flows

We investigate blow-up criteria for the local in time classical solution of the 3D incompressible nematic liquid crystal flows via the pressure and the orientation field. More precisely, we prove that 0 < T-* < +infinity is the maximal time interval if and only if integral(T*)(0) parallel to P parallel to(beta)(L alpha) + parallel to del d parallel to(8)(L4) dt=infinity, with 3/alpha +2/beta <= 2, and 3/2 < alpha <= infinity and integral(T*)(0) parallel to del P parallel to(beta)(L alpha) + parallel to del d parallel to(8)(L4) dt=infinity, with 3/alpha +2/beta <= 3, and 1 < alpha <= infinity.