SIAM Journal on Mathematical Analysis
We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 Society for Industrial and Applied Mathematics.
Original Publication Citation
Cavaterra, C., Rocca, E., Wu, H., & Xu, X. (2016). Global strong solutions of the full Navier-Stokes and Q-tensor system for nematic liquid crystal flows in two dimensions. SIAM Journal on Mathematical Analysis, 48(2), 1368-1399. doi:10.1137/15M1048550
Cavaterra, Cecilia; Rocca, Elisabetta; Wu, Hao; and Xu, Xiang, "Global Strong Solutions of the Full Navier-Stokes and Q-Tensor System for Nematic Liquid Crystal Flows in Two Dimensions" (2016). Mathematics & Statistics Faculty Publications. 12.