Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals
arXiv:1805.02439
Abstract
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with an Allen-Cahn system for the Q-tensor variable. This problem has a dissipative in time free-energy which leads, in particular, to prove the existence of global in time weak solutions. We analyze the large-time behavior of the weak solutions. By using a Lojasiewicz-Simon's result, we prove the convergence as time goes to infinity of the whole trajectory to a single equilibrium.
arXiv comment14 pages
References in corpus (3)
- Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties
- Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow
- Strong solutions for the Beris-Edwards model for nematic liquid crystals with homogeneous Dirichlet boundary conditions