Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow
Analysis of PDEs
2012-10-09 v1
Abstract
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as a reasonable approximation of the well-known Ericksen--Leslie system. Taking advantage of previous well-posedness results and proving suitable dissipative estimates, here we show that the system endowed with periodic boundary conditions is a dissipative dynamical system with a smooth global attractor of finite fractal dimension.
Cite
@article{arxiv.1210.2124,
title = {Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow},
author = {Maurizio Grasselli and Hao Wu},
journal= {arXiv preprint arXiv:1210.2124},
year = {2012}
}