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We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is…

Analysis of PDEs · Mathematics 2026-05-08 Prince Romeo Mensah

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…

Analysis of PDEs · Mathematics 2015-04-07 Matthias Hieber , Jan Pruess

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…

Analysis of PDEs · Mathematics 2013-09-03 Mimi Dai

The Ericksen-Leslie model for nematic liquid crystal flows in case of an isothermal and incompressible fluid with general Leslie stress and anisotropic elasticity, i.e. with general Ericksen stress tensor, is shown for the first time to be…

Analysis of PDEs · Mathematics 2025-11-25 Matthias Hieber , Jinkai Li , Mathias Wilke

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…

Analysis of PDEs · Mathematics 2020-03-13 Yuan Cai , Wei Wang

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…

Analysis of PDEs · Mathematics 2023-02-24 Tao Huang , Chengyuan Qu

In this paper, we prove the existence and uniqueness of local strong solutions of the hydrodynamics of nematic liquid crystals system under the initial data satisfying a natural compatibility condition. Also the global strong solutions of…

Functional Analysis · Mathematics 2011-07-01 Xiangao Liu , Lanming Liu , Yihang Hao

In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The…

Analysis of PDEs · Mathematics 2025-09-22 Felix Brandt , Matthias Hieber , Arnab Roy

In this note we prove the existence and uniqueness of local maximal smooth solution of the stochastic simplified Ericksen-Leslie systems modelling the dynamics of nematic liquid crystals under stochastic perturbations.

Analysis of PDEs · Mathematics 2020-11-03 Zdzislaw Brzezniak , Erika Hausenblas , Paul Razafimandimby

Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…

Analysis of PDEs · Mathematics 2015-05-30 Mimi Dai , Jie Qing , Maria E. Schonbek

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…

Analysis of PDEs · Mathematics 2010-11-04 Hao Wu

In this paper we establish the uniformity property of a simplified Ericksen-Leslie system modelling the hydrodynamics of nematic liquid crystals on the two dimensional unit sphere $S^2$, namely the uniform convergence in $L^2$ to a steady…

Analysis of PDEs · Mathematics 2013-08-20 Changyou Wang , Xiang Xu

The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…

Analysis of PDEs · Mathematics 2024-09-19 Daniele Barbera , Vladimir Georgiev

The work deals with the Ericksen-Leslie System for nematic liquid crystals on the whole space. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere.…

Analysis of PDEs · Mathematics 2023-05-24 Daniele Barbera , Vladimir Georgiev

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie…

Analysis of PDEs · Mathematics 2013-02-26 Hao Wu , Xiang Xu , Chun Liu

The Ericksen-Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally well-posed…

Analysis of PDEs · Mathematics 2016-07-25 Matthias Hieber , Jan Prüss

We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we…

Analysis of PDEs · Mathematics 2012-10-05 Guochun Wu , Zhong Tan

This paper establishes the global well-posedness and long-time dynamics of the general Ericksen--Leslie system for isotropic nematic liquid crystals under a constant magnetic field. On the two-dimensional torus $\mathbb{T}^2$, a liquid…

Analysis of PDEs · Mathematics 2025-11-07 Qingtong Wu

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…

Analysis of PDEs · Mathematics 2013-02-20 Matthias Hieber , Manuel Nesensohn , Jan Prüss , Katharina Schade

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…

Analysis of PDEs · Mathematics 2012-12-03 Shengquan Liu , Jianwen Zhang
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