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| We consider a general family of regularized flows for the simplified Ericksen-Leslie (RSEL) model for the hydrodynamics of liquid crystals in 2 and 3-dimensional compact Riemannian manifolds. The system contains the Navier-Stokes equations, the Navier-Stokes-Voight and the Navier-Stokes alpha-model equations as special cases, and many others. We establish existence, stability, regularity results and singular perturbation results, and we also show the existence of a global attractor and exponential attractor for the general family. Then we establish precise conditions under which each trajectory converges to a single equilibrium by means of a Lojasiewicz-Simon inequality. |
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