Blanca Climent-Ezquerra, Francisco Guillén-González
Published 2018-05-07Version 1
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.
Convergence of approximate deconvolution models to the filtered Navier-Stokes Equations
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
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