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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.

偏微分方程分析 · 数学 2020-11-03 Zdzislaw Brzezniak , Erika Hausenblas , Paul Razafimandimby

There are two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie director theory and the Eringen micropolar approach. Up to this day, these two descriptions have remained distinct in spite of several attempts to…

软凝聚态物质 · 物理学 2013-11-05 François Gay-Balmaz , Tudor S. Ratiu , Cesare Tronci

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…

偏微分方程分析 · 数学 2024-09-04 Tim Binz , Felix Brandt , Matthias Hieber , Arnab Roy

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…

偏微分方程分析 · 数学 2025-11-07 Qingtong Wu

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…

软凝聚态物质 · 物理学 2013-01-08 Hossein Pourmatin , Amit Acharya , Kaushik Dayal

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…

偏微分方程分析 · 数学 2026-01-06 Kuntal Bhandari , Apala Majumdar , Šárka Nečasová

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…

泛函分析 · 数学 2011-07-01 Xiangao Liu , Lanming Liu , Yihang Hao

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…

偏微分方程分析 · 数学 2013-05-07 Maurizio Grasselli , Hao Wu

In this paper, we investigate the Beris-Edwards system for both biaxial and uniaxial $Q$-tensors with a general Landau-de Gennes energy density depending on four non-zero elastic constants. We prove existence of the strong solution of the…

偏微分方程分析 · 数学 2025-09-29 Zhewen Feng , Min-Chun Hong , Yu Mei

We consider the compressible Ericksen-Leslie system of liquid crystal flows in one dimension. A global weak solution is constructed with initial density $\rho_0\geq 0$ and $\rho_0\in L^\gamma$ for $\gamma>1$.

偏微分方程分析 · 数学 2020-06-18 Huajun Gong , Tao Huang , Changyou Wang

In this paper, we derive a new model for the description of liquid crystalline flows. While microscopic Doi type models suffer from the high dimensionality of the underlying product space, the more macroscopic Ericksen--Leslie type models…

偏微分方程分析 · 数学 2021-03-04 Stefan Metzger

In this paper, we will establish the global existence of a suitable weak solution to the Erickson--Leslie system modeling hydrodynamics of nematic liquid crystal flows with kinematic transports for molecules of various shapes in…

偏微分方程分析 · 数学 2021-07-07 Hengrong Du , Changyou Wang

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…

软凝聚态物质 · 物理学 2010-10-18 François Gay-Balmaz , Cesare Tronci

We present a robust discretization of the Ericksen model of liquid crystals with variable degree of orientation coupled with colloidal effects and electric fields. The total energy consists of the Ericksen energy, a weak anchoring (or…

数值分析 · 数学 2017-11-22 Ricardo H. Nochetto , Shawn W. Walker , Wujun Zhang

In this paper, we prove the singularity formation for Poiseuille laminar flow of full Ericksen-Leslie system modeling nematic liquid crystal flows in dimension two. The singularity is due to the geometric effect at the origin.

偏微分方程分析 · 数学 2023-05-09 Geng Chen , Tao Huang , Xiang Xu

For any smooth domain $\Omega\subset \mathbb{R}^3$, we establish the existence of a global weak solution $(\mathbf{u},\mathbf{d}, \theta)$ to the simplified, non-isothermal Ericksen-Leslie system modeling the hydrodynamic motion of nematic…

偏微分方程分析 · 数学 2020-01-07 Hengrong Du , Yimei Li , Changyou Wang

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…

偏微分方程分析 · 数学 2026-05-19 Hengrong Du , Fizay-Noah Lee , Gieri Simonett

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…

偏微分方程分析 · 数学 2012-12-03 Shengquan Liu , Jianwen Zhang

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…

偏微分方程分析 · 数学 2012-11-27 Qing Chen , Zhong Tan , Guochun Wu

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…

偏微分方程分析 · 数学 2014-03-21 Fei Jiang , Song Jiang , Dehua Wang