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We consider the temporal decay estimates for weak solutions to thetwo-dimensional nematic liquid crystal flows, and we show that the energy normof 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 initialdata. We also show the exact rate of the decay (uniform decay) of the energynorm of the global weak solution.

On the temporal decay of solutions to the two-dimensional nematic liquid crystal flows