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arXiv · 1409.4292

On a regularized family of models for the full Ericksen-Leslie system

Ciprian G. Gal·Louis Tebou
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Abstract

We consider a general family of regularized systems for the full Ericksen-Leslie model for the hydrodynamics of liquid crystals in $n$-dimensional compact Riemannian manifolds, $n$=2,3. The system we consider consists of a regularized family of Navier-Stokes equations (including the Navier Stokes-$\alpha $-like equation, the Leray-$\alpha $ equation, the Modified Leray-$\alpha $ equation, the Simplified Bardina model, the Navier Stokes-Voigt model and the Navier-Stokes equation) for the fluid velocity $u$ suitably coupled with a parabolic equation for the director field $d$. We establish existence, stability and regularity results for this family. We also show the existence of a finite dimensional global attractor for our general model, and then establish sufficiently general conditions under which each trajectory converges to a single equilibrium by means of a Lojasiewicz-Simon inequality.

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Ciprian G. Gal, Louis Tebou. 2014-09-15. On a regularized family of models for the full Ericksen-Leslie system. https://doi.org/10.1016/j.na.2015.07.012

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