# 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}
}
• Published 26 September 2014
• Mathematics
• Asymptot. Anal.
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
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
• Mathematics
Archive 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
• Mathematics
Archive 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
• 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
• Mathematics
SIAM 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.
• 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
• Mimi Dai
• Mathematics
SIAM 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.
• Xiang Xu
• Chemistry
Electronic 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
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
• Mathematics
Archive 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

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics
• 2012
We study a complex non-Newtonian fluid that models the flowof nematic liquid crystals. The fluid is described by a system that couples a forced Navier–Stokes system with a parabolic-type system. We
• Physics
• 1994
PART 1: THEORY Introduction 1. Symplectic geometry in optics 2. Hamiltonian mechanics of discrete particle systems 3. Equilibrium thermodynamics 4. Poisson brackets in continuous media 5.
• Mathematics
SIAM J. Math. Anal.
• 2011
Under certain conditions it is proved the global existence of weak solutions in dimension two or three and the existence of global regular solutions in Dimension two and the weak-strong uniqueness of the solutions, for sufficiently regular initial data.
Etude des solutions du probleme de Cauchy pour de grandes valeurs du temps dans le cas d'equations de Navier-Stokes a 2 et 3 dimensions d'espace
• Mark Wilkinson
• Mathematics
• 2015
We study the existence, regularity and so-called ‘strict physicality’ of global weak solutions of a Beris–Edwards system which is proposed as a model for the incompressible flow of nematic liquid
It is shown that for a certain class of initial data the solutions u(x, t) to the 2D and 3D Navier-Stokes equations admit an algebraic lower bound on the energy decay.
• E. KirrMark Wilkinson
• Mathematics
• 2012
In this article, we investigate the long time behaviour of a correlation function $$c_{\mu _{0}}$$cμ0 which is associated with a nematic liquid crystal system that is undergoing an isotropic-nematic
• Mathematics
• 1983
1. The Main Result; Examples . . . . . . . . . . . . . . . . . . . . . . . 316 2. Necessary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 319 3. The Constrained Minimization Method .
• W. Rother
• Mathematics
Differential and Integral Equations
• 1992