Related papers: Weak compactness of simplified nematic liquid flow…
We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the…
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…
Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…
We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of…
We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence…
In this paper we consider the 2D Ericksen-Leslie equations which describes the hydrodynamics of nematic Liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or…
Ericksen and Leslie established a theory to model the flow of nematic liquid crystals. This paper is devoted to the Cauchy Problem of a simplified version of their system, which retains most of the properties of the original one. We…
We present a continuous and a discontinuous linear Finite Element method based on a predictor-corrector scheme for the numerical approximation of the Ericksen-Leslie equations, a model for nematic liquid crystal flow including a non-convex…
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…
Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale…
We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. We first focus on…
Weak-strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy. To overcome the difficulties caused by the molecular…
We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba-Jaumann derivative. Moreover, the stress…
In this paper, we study the long-time behavior of full Ericksen-Leslie system modeling the hydrodynamics of nematic liquid crystals between two dimensional unit spheres. Under a weaker assumption for Leslie's coefficients, we give the key…
We study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept,…
In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies…
In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for…
In this paper, we study the Cauchy problem of the Poiseuille flow of full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of a parabolic equation for the velocity and a quasilinear wave equation for the…
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable, and allows the formation of various defects with finite energy. We propose a simple but novel finite element approximation…
For $n\ge 3$ and $0<\epsilon\le 1$, let $\Omega\subset\mathbb R^n$ be a bounded smooth domain and $u_\epsilon:\Omega \subset\R^n\to \mathbb R^2$ solve the Ginzburg-Landau equation under the weak anchoring boundary condition: $$\begin{cases}…