  We consider the temporal decay estimates for weak solutions to the
two-dimensional nematic liquid crystal flows, and we show that the energy norm
of a global weak solution has non-uniform decay \begin{align*}
\|u(t)\|_{L^{2}}+\|\nabla d(t)\|_{L^{2}}\rightarrow 0\quad \text{ as }
t\rightarrow \infty, \end{align*} under suitable conditions on the initial
data. We also show the exact rate of the decay (uniform decay) of the energy
norm of the global weak solution.
