Global strong solutions of the full Navier-Stokes and \(Q\)-tensor system for nematic liquid crystal flows in two dimensions (Q2802688)

In this paper, the authors study a full Navier-Stokes and \(Q\)-tensor system for incompressible liquid crystal flows of nematic type. In the two-dimensional periodic case they proved the existence and uniqueness of global strong solutions that are uniformly bounded in time. To get this result it was not necessary to assume some smallness on the physical parameter \(\varepsilon\) which measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Furthermore, it was shown in the paper that the asymptotic limit for each global strong solution is unique. Finally, the authors of this study prove an uniform estimate on the convergence rate.NEWLINENEWLINEThe paper is self-contained and all necessary tools are described clearly. The bibliography contains 42 items.