Jeffrey-Hamel flow of Leslie-Ericksen nematic liquids

Numerical Approximation of Nematic Liquid Crystal Flows Governed by the Ericksen–leslie Equations

Numerical approximation of the flow of liquid crystals governed by the Ericksen–Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.

Well-posedness of the full Ericksen–Leslie model of nematic liquid crystals

The Ericksen–Leslie model of nematic liquid crystals is a coupled system between the Navier–Stokes and the Ginzburg–Landau equations. We show here the local well-posedness for this problem for any initial data regular enough, by a fixed point approach relying on some weak continuity properties in a suitable functional setting. By showing the existence of an appropriate local Lyapunov functional...

Well-posedness of the Ericksen-leslie System

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the GinzburgLandau approximation, we construct an approximate system with the dissipated energy based on a new formulation of th...

A fundamental improvement to Ericksen-Leslie kinematics

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body for...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow