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

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 ∥u(t)∥L2+∥∇d(t)∥L2→0ast→∞,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.