Global strong solutions of the full Navier--Stokes and $Q$-tensor system for nematic liquid crystal flows in $2D$: Existence and long-time behavior
- Cavaterra, Cecilia
- Rocca, Elisabetta
- Wu, Hao
- Xu, Xiang
2010 Mathematics Subject Classification
- 35B44 35D30 35K45 35Q30 76A15
- Nematic liquid crystal flow, Q-tensor system, global strong solution, uniqueness of asymptotic limit
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 $xi$ 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.
- SIAM J. Math. Anal., 48 (2016) pp. 1368--1399.