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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

The Cauchy problem for the three-dimensional compressible flow of nematic liquid crystals is considered. Existence and uniqueness of the global strong solution are established in critical Besov spaces provided that the initial datum is…

Analysis of PDEs · Mathematics 2024-08-21 Xianpeng Hu , Hao Wu

In this paper, we study the uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the compressible…

Analysis of PDEs · Mathematics 2016-07-21 Jincheng Gao , Boling Guo , Yaqing Liu

In this paper, we consider the non-isothermal model for incompressible flow of nematic liquid crystals in three dimensions and prove the local existence and uniqueness of the strong solution with periodic initial conditions on $…

Analysis of PDEs · Mathematics 2014-12-03 Shijin Ding , Quanrong Li

The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial…

Analysis of PDEs · Mathematics 2011-12-25 Xiaoli Li , Dehua Wang

The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is…

Analysis of PDEs · Mathematics 2012-02-07 Xiaoli Li , Dehua Wang

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the…

Analysis of PDEs · Mathematics 2016-11-25 Tao Huang , Changyou Wang , Huanyao Wen

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

Analysis of PDEs · Mathematics 2023-08-09 Yannick Sire , Yantao Wu , Yifu Zhou

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…

Analysis of PDEs · Mathematics 2013-05-07 Maurizio Grasselli , Hao Wu

This paper concerns the initial boundary value problem of three-dimensional inhomogeneous incompressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density…

Analysis of PDEs · Mathematics 2024-10-17 Jiaxu Li , Yu Mei , Rong Zhang

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

In this paper we provide a sufficient condition, in terms of the horizontal gradient of two horizontal velocity components and the gradient of liquid crystal molecular orientation field, for the breakdown of local in time strong solutions…

Analysis of PDEs · Mathematics 2016-05-03 Jihong Zhao

In this paper, we investigate the Cauchy problem for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the time decay rates for compressible nematic liquid crystal flows by the method…

Analysis of PDEs · Mathematics 2015-03-11 Jincheng Gao , Qiang Tao , Zheng-an Yao

We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly…

Analysis of PDEs · Mathematics 2023-07-28 Cecilia Cavaterra , Elisabetta Rocca , Hao Wu , Xiang Xu

In this paper, we consider the initial and boundary value problem of a simplified compressible nematic liquid crystal flow in $\Omega\subset\mathbb R^3$. We establish the existence of global weak solutions, provided the initial…

Analysis of PDEs · Mathematics 2014-08-20 Junyu Lin , Baishun Lai , Changyou Wang

We study the three-dimensional Cauchy problem for a non-isothermal compressible nematic liquid crystal system with far-field vacuum. By deriving refined energy estimates and exploiting the coupled structure of the equations, we establish…

Analysis of PDEs · Mathematics 2025-12-30 Lin Xu , Xin Zhong

The present paper is dedicated to the global large solutions and incompressible limit for the compressible flow of liquid crystals under the assumption on almost constant density and large volume viscosity. The result is based on Fourier…

Analysis of PDEs · Mathematics 2018-05-29 Xiaoping Zhai , Zhi-min Chen

In this paper, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on $\mathbb T^2$, based on a new approximate system which is different from the classical Ginzburg-Landau approximation.…

Analysis of PDEs · Mathematics 2013-10-29 Jinkai Li , Zhouping Xin

In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid…

Analysis of PDEs · Mathematics 2012-11-27 Qing Chen , Zhong Tan , Guochun Wu

Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analysed. We derive the thin-film Ericksen-Leslie equations that govern…

Soft Condensed Matter · Physics 2024-09-10 Joseph R. L. Cousins , Nigel J. Mottram , Stephen K. Wilson