Climent Ezquerra, María BlancaGuillén González, Francisco Manuel2022-11-112022-11-112018-05-07Climent Ezquerra, M.B. y Guillén González, F.M. (2018). Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals. https://doi.org/10.48550/arXiv.1805.02439.https://hdl.handle.net/11441/139301We 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.application/pdf14 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Liquid crystalsAllen-Cahn-Navier-Stokes systemLarge-time behavior for dissipative systemsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.48550/arXiv.1805.02439