Dynamic theory for incompressible smectic-A liquid crystals: existence and regularity
type: Item
instance of: scholarly article
title: Dynamic theory for incompressible smectic-A liquid crystals: existence and regularity
zbMATH Open document ID: 1021.35083
author: Chun Liu
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The author studies the following evolution system that models fluids which are under influence of internal molecule layers, that is: \[ \begin{aligned} & \rho_t+\nabla\cdot (\rho v)=0,\\ & \rho\dot v+\nabla(-pI+\sigma^e+\sigma^d),\\ & \dot\varphi = \lambda(\nabla\cdot (\xi \nabla \varphi)-K\Delta^2\varphi),\end{aligned} \] where \(\rho:\Omega\times [0,\infty)\to\mathbb{R}\) is the density of materials, \(p\) is the scalar function describing the fluid pressure, \(v:\Omega\times [0,\infty)\to\mathbb{R}^3(\mathbb{R}^2)\) is the flow velocity, and \(\varphi:\Omega\times [0,\infty)\to\mathbb{R}\) is the layer variable. Here \(\Omega\) is a bounded domain in \(\mathbb{R}^3(\mathbb{R}^2)\). The author proves existence of global weak solutions. Moreover, he discusses some regularity and stability results.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1492660
zbMATH Keywords: internal molecule layers
zbMATH Keywords: stability
zbMATH Keywords: existence
zbMATH Keywords: regularity
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.2000.6.591
OpenAlex ID: W2092799013
DOI: 10.3934/DCDS.2000.6.591
Recommended article: Dynamic theory for smectic A liquid crystals
Recommended article: Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations
Recommended article: Nonlinear continuum theory of smectic-\(A\) liquid crystals
Recommended article: Q4365689
Recommended article: Existence in non‐smooth domain for compressible liquid crystals
Recommended article: A hydrodynamic theory of compressible SmC* liquid crystals
Recommended article: A smectic liquid crystal model in the periodic setting
Recommended article: Finite Dimensional Reduction and Convergence to Equilibrium for Incompressible Smectic-A Liquid Crystal Flows
Recommended article: On well-posedness and large time behavior for smectic-a liquid crystals equations in \(\mathbb{R}^3\)
Recommended article: Existence of solutions to boundary value problems for smectic liquid crystals
description: scientific article; zbMATH DE number 1492660