scholarly journals On Regularity Criteria for the Two-Dimensional Generalized Liquid Crystal Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yanan Wang ◽  
Zaihong Jiang
Keyword(s):  
Liquid Crystal ◽  
Global Existence ◽  
Existence Results ◽  
Regularity Criteria ◽  
Two Dimensional ◽  
Crystal Model

We establish the regularity criteria for the two-dimensional generalized liquid crystal model. It turns out that the global existence results satisfy our regularity criteria naturally.

Global regularity for the 2D liquid crystal model with mixed partial viscosity

2015 ◽  
Vol 13 (02) ◽  
pp. 185-200 ◽  
Author(s):  
Jishan Fan ◽  
Faris Saeed Alzahrani ◽  
Tasawar Hayat ◽  
Gen Nakamura ◽  
Yong Zhou
Keyword(s):  
Liquid Crystal ◽  
Global Existence ◽  
Global Regularity ◽  
Strong Solutions ◽  
Regularity Criteria ◽  
Crystal Model

This paper proves the global existence of strong solutions of the 2D liquid crystal model when ν1= k2= 0, ν2= k1= 1 or ν1= k2= 1, ν2= k1= 0. We also prove some regularity criteria when ν1= k1= 1, ν2= k2= 0 or ν1= k1= 0, ν2= k2= 1.

scholarly journals Instability of point defects in a two-dimensional nematic liquid crystal model

2016 ◽  
Vol 33 (4) ◽  
pp. 1131-1152 ◽  
Author(s):  
Radu Ignat ◽  
Luc Nguyen ◽  
Valeriy Slastikov ◽  
Arghir Zarnescu
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Point Defects ◽  
Two Dimensional ◽  
Crystal Model

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

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