# On asymptotic isotropy for a hydrodynamic model of liquid crystals

@article{Dai2014OnAI, title={On asymptotic isotropy for a hydrodynamic model of liquid crystals}, author={Mimi Dai and Eduard Feireisl and Elisabetta Rocca and Giulio Schimperna and Maria E. Schonbek}, journal={Asymptot. Anal.}, year={2014}, volume={97}, pages={189-210} }

We study a PDE system describing the motion of liquid crystals by means of the Q−tensor description for the crystals coupled with the incompressible Navier-Stokes system. Using the method of Fourier splitting, we show that solutions of the system tend to the isotropic state at the rate (1+ t)−β as t→∞ for a certain β > 1 2 .

## 21 Citations

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

- MathematicsMathematics
- 2019

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…

### Dynamics and Flow Effects in the Beris-Edwards System Modeling Nematic Liquid Crystals

- MathematicsArchive for Rational Mechanics and Analysis
- 2018

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic…

### Dynamics and Flow Effects in the Beris-Edwards System Modeling Nematic Liquid Crystals

- MathematicsArchive for Rational Mechanics and Analysis
- 2018

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic…

### Large Time Behavior of the Navier-Stokes Flow

- Mathematics
- 2018

Different results related to the asymptotic behavior of incompressible fluid equations are analyzed as time tends to infinity. The main focus is on the solutions to the Navier-Stokes equations, but…

### Global Strong Solutions of the Full Navier-Stokes and Q-Tensor System for Nematic Liquid Crystal Flows in Two Dimensions

- MathematicsSIAM J. Math. Anal.
- 2016

In the two dimensional periodic case, it is proved the existence and uniqueness of global strong solutions that are uniformly bounded in time and the uniqueness of asymptotic limit for each global strong solution as time goes to infinity.

### On the initial boundary value problem of a Navier-Stokes/$Q$-tensor model for liquid crystals

- Mathematics
- 2016

This work is concerned with the solvability of a Navier-Stokes/$Q$-tensor coupled system modeling the nematic liquid crystal flow on a bounded domain in three dimensional Euclidian space with strong…

### Regularity Problem for the Nematic LCD System with Q-tensor in ℝ3

- MathematicsSIAM J. Math. Anal.
- 2017

Applying a wavenumber splitting method, it is shown that a solution does not blow-up under certain extended Beale-Kato-Majda condition solely imposed on velocity.

### Recent analytic development of the dynamic $ Q $-tensor theory for nematic liquid crystals

- ChemistryElectronic Research Archive
- 2022

Liquid crystals are a typical type of soft matter that are intermediate between conventional crystalline solids and isotropic fluids. The nematic phase is the simplest liquid crystal phase, and has…

### Regularity problem for the nematic LCD system with Q-tensor in $\mathbb R^3$

- Mathematics
- 2016

We study the regularity problem of a nematic liquid crystal model with local configuration represented by Q-tensor in three dimensions. It was an open question whether the classical Prodi-Serrin…

### Dynamics of the Ericksen–Leslie Equations with General Leslie Stress II: The Compressible Isotropic Case

- MathematicsArchive for Rational Mechanics and Analysis
- 2019

In this article, the non-isothermal compressible Ericksen–Leslie system for nematic liquid crystals subject to general Leslie stress is considered. It is shown that this system is locally well-posed…

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