scholarly journals Long-time behavior for nonlinear hydrodynamic system modeling the nematic liquid crystal flows

2010 ◽  
Vol 26 (1) ◽  
pp. 379-396 ◽  
Author(s):  
Hao Wu ◽  
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
System Modeling ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Hydrodynamic System ◽  
Long Time ◽  
Nematic Liquid Crystal Flows

scholarly journals Long-time behavior of global weak solutions for a Beris-Edwards type model of nematic liquid crystals

2020 ◽  
Author(s):  
Blanca CLIMENT-EZQUERRA ◽  
Francisco Guillen-Gonzalez
Keyword(s):  
Liquid Crystal ◽  
Stokes System ◽  
System Modeling ◽  
Fluid Velocity ◽  
Global Solutions ◽  
Navier Stokes ◽  
Type Model ◽  
Time Behavior ◽  
Infinite Time ◽  
Long Time

We consider a generalization of the standard Beris-Edwards system modeling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with an evolution equation for the Q-tensors variable describing the direction of liquid crystal molecules. The convergence at infinite time for global solutions is studied and we prove that whole trajectory goes to a single equilibrium by using a Lojasiewicz-Simon’s result.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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