We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R. We first prove the local existence of unique strong solutions provided that the initial data ρ0, u0, d0 are sufficiently regular and satisfy a natural compatibility condition. The initial density function ρ0 may vanish on an open subset (i.e., an initial vacuu...

We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls. We are also able to include material p...

We consider the Poiseuille flow of nematic liquid crystals via full Ericksen-Leslie model. The model is described by a coupled system consisting heat equation and quasilinear wave equation. In this paper, we will construct an example with finite time cusp singularity due to quasilinearity equation, extended from earlier result on special case.

Abstract. Here we investigate the kinematic transports of the defects in the nematic liquid crystal system by numerical experiments. The model is a shear flow case of the viscoelastic continuummodel simplified from the Ericksen-Leslie system. The numerical experiments are carried out by using a differencemethod. Based on these numerical experiments we find some interesting and important relatio...

Capillary microflows of liquid crystal phases are central to material, biological and bio-inspired systems. Despite their fundamental applied significance, a detailed understanding the stationary behavior nematic crystals (NLC-s) in cylindrical capillaries is still lacking. Here, using numerical simulations based on continuum theory Leslie, Ericksen, Parodi, we investigate NLC flows within poss...

We study a system of nonlinear second order ordinary differential equations modeling Poiseuille flow of liquid crystals with variable degree of orientation, at the limit of large Ericksen number. The system is singularly perturbed and degenerate, and as a result the solutions are highly oscillatory. We obtain the relations satisfied by the Young measures generated by sequences of weak solutions...