Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow
arXiv:1210.2124 · doi:10.1007/s00033-011-0157-9
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.
References in corpus (3)
Cited by in corpus (12)
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- On a 3D isothermal model for nematic liquid crystals accounting for stretching terms
- Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D
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- Long-time behavior for a hydrodynamic model on nematic liquid crystal flows with asymptotic stabilizing boundary condition and external force
- Random attractor for the 2D stochastic nematic liquid crystals flows with multiplicative noise
- Existence of regular solutions to the full Liquid Crystal System
- On the long-time behavior of some mathematical models for nematic liquid crystals
- Global weak solution and blow-up criterion of the general Ericksen-Leslie system for nematic liquid crystal flows
- Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals