On asymptotic isotropy for a hydrodynamic model of liquid crystals

  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.},
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 . 

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

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

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

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

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

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

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

  • 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.

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

  • 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

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

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

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



Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System

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

Thermodynamics of flowing systems : with internal microstructure

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.

Global Existence and Regularity for the Full Coupled Navier-Stokes and Q-Tensor System

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.

Large time behaviour of solutions to the navier-stokes equations

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

Strictly Physical Global Weak Solutions of a Navier–Stokes Q-tensor System with Singular Potential

  • 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

Lower bounds of rates of decay for solutions to the Navier-Stokes equations

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.

Dynamic Statistical Scaling in the Landau–de Gennes Theory of Nematic Liquid Crystals

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

Nonlinear scalar field equations, I existence of a ground state

1. The Main Result; Examples . . . . . . . . . . . . . . . . . . . . . . . 316 2. Necessary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 319 3. The Constrained Minimization Method .

Nonlinear scalar field equations

  • W. Rother
  • Mathematics
    Differential and Integral Equations
  • 1992

Sound Propagation in Stratified Fluids