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

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.

34 pages; Nonlinear Analysis 07/2015. arXiv admin note: text overlap with arXiv:1409.4293; text overlap with arXiv:0901.4412 by other authors

References in corpus (2)

• On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability
• On a regularized family of models for homogeneous incompressible two-phase flows