Related papers: Nematic liquid crystal flow with partially free bo…
In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen--Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier--Stokes…
In this paper, we consider a simplified Ericksen-Leslie model for the nematic liquid crystal flow. The evolution system consists of the Navier-Stokes equations coupled with a convective Ginzburg-Landau type equation for the averaged…
We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…
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…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations. We prove the global existence of classical solution with…
We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…
We present explicit expressions of the helicity conservation in nematic liquid crystal flows, for both the Ericksen-Leslie and Landau-de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation…
We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions…
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…
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…
In this work, we study the Cauchy problem of Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of two partial differential equations: One is a quasi-linear wave equation for the…
We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model. The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation. In this paper, we will construct an…
In this paper, we study the initial-boundary value problem for the Poiseuille flow of hyperbolic-parabolic Ericksen-Leslie model of nematic liquid crystals in one space dimension. Due to the quasilinearity, the solution of this model in…
We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain $\Omega\subset \mathbb{R}^N$, where N=2…
In the first part of this paper, we establish global existence of solutions of the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The liquid crystal flow is a prototype of equations from the Ericksen-Leslie system in…
The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore, hydrodynamic electronics requires the detailed understanding of electron flow in finite geometries. The…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified…