  In this paper, we consider the short time classical solution to a simplified
hydrodynamic flow modeling incompressible, nematic liquid crystal materials in
dimension three. We establish a criterion for possible breakdown of such
solutions at a finite time. More precisely, if $(u,d)$ is smooth up to time $T$
provided that $\int_0^T|\nabla\times u(t,\cdot)|_{BMO(\mathbb R^3)}+|\nabla
d(t,\cdot)|^8_{L^4(\mathbb R^3)}dt<\infty $
