scholarly journals Global Existence of Strong Solutions for Beris–Edwards’s Liquid Crystal System in Dimension Three

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 972
Author(s):  
Luo ◽  
Li ◽  
Zhao
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Global Existence ◽  
Evolution Equation ◽  
Bounded Domain ◽  
Incompressible Flow ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupling System ◽  
Liquid Crystal System

We consider a system, established by Beris and Edwards in the Q-tensor framework,modeling the incompressible flow of nematic liquid crystals. The coupling system consists of theNavier–Stokes equation and the evolution equation for the Q-tensor. We prove the global existenceof strong solutions in a three-dimensional bounded domain with homogeneous Dirichlet boundaryconditions, under the assumption that the viscosity is sufficiently large.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

scholarly journals Strong solutions to the compressible liquid crystal system

2012 ◽  
Vol 257 (1) ◽  
pp. 37-52 ◽  
Author(s):  
Yu-Ming Chu ◽  
Xian-Gao Liu ◽  
Xiao Liu
Keyword(s):  
Liquid Crystal ◽  
Strong Solutions ◽  
Compressible Liquid ◽  
Crystal System ◽  
Liquid Crystal System

Global existence of the 3D rotating second grade fluid system

2020 ◽  
pp. 1-32
Author(s):  
Basma Jaffal-Mourtada
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Fluid System ◽  
Forcing Term ◽  
First Case ◽  
Grade Fluid

We consider the equations of a rotating incompressible non-Newtonian fluid flow of grade two in a three dimensional torus. We prove two different results of global existence of strong solutions. In the first case, we consider that the elasticity coefficient α is arbitrary and we suppose that the third components of the vertical average of the initial data and of the forcing term are small compared to the horizontal components. In the second case, we consider a forcing term and initial data of arbitrary size but we restrict the size of α. In both cases, we show that the limit system is composed of a linear system and a second grade fluid system with two variables and three components.

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