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Finite--dimensional global attractor for a system modeling the 2D nematic liquid crystal flow

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.

preprint2012arXivOpen access
Maurizio GrasselliHao Wu
math.AP
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Maurizio GrasselliHao Wu

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