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Finite-dimensional global attractor for a system modeling the \(2D\) nematic liquid crystal flow. (English) Zbl 1242.35057
The authors 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 the authors show that the system endowed with periodic boundary conditions is a dissipative dynamical system with a smooth global attractor of finite fractal dimension.

MSC:
35B41 Attractors
35Q35 PDEs in connection with fluid mechanics
76A15 Liquid crystals
76D05 Navier-Stokes equations for incompressible viscous fluids
35K57 Reaction-diffusion equations
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