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This paper investigates the global well-posedness and large-time behavior of 3D incompressible active liquid crystals under constant activity, modeled by a coupled system of forced incompressible Navier-Stokes equations for the velocity and…

Analysis of PDEs · Mathematics 2026-05-18 Fan Yang , Xiongfeng Yang

A complex non-Newtonian fluid models the nematic liquid crystal flows confined in a bounded domain in $\mathbb{R}^3$ is considered. The system is a forced incompressible Navier-Stokes equation coupled with a parabolic type Q-tensor flows.…

Analysis of PDEs · Mathematics 2017-01-17 Yao Xiao

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 reaction-convection-diffusion equation for the Q-tensors…

Analysis of PDEs · Mathematics 2023-07-28 Hao Wu , Xiang Xu , Arghir Zarnescu

We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with…

Analysis of PDEs · Mathematics 2018-05-08 Blanca Climent-Ezquerra , Francisco Guillén-González

The Ericksen-Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress is studied in the case of a non-isothermal and incompressible fluid. This system is shown to be locally well-posed…

Analysis of PDEs · Mathematics 2016-07-25 Matthias Hieber , Jan Prüss

We give a regularity criterion for a $Q$-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary conditions for the tensor $Q$. Starting of a criterion only imposed on the velocity field ${\bf u}$ two results are…

Analysis of PDEs · Mathematics 2014-11-21 Francisco Guillén-González , María Ángeles Rodríguez-Bellido

We study a fluid-structure interaction problem describing movement of a rigid body inside a bounded domain filled by a viscous fluid. The fluid is modelled by the generalized incompressible Naiver-Stokes equations which include cases of…

Analysis of PDEs · Mathematics 2021-09-22 Hind Al Baba , Amrita Ghosh , Boris Muha , Sarka Necasova

This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the…

Numerical Analysis · Mathematics 2025-06-06 Heiko Gimperlein , Ruma R. Maity

In this paper, we consider the model describing viscous incompressible liquid crystal flows, called the Beris-Edwards model, in the half-space.This model is a coupled system by the Navier-Stokes equations with the evolution equation of the…

Analysis of PDEs · Mathematics 2024-07-01 Daniele Barbera , Miho Murata

The goal of this work is to rigorously study the zero inertia limit for the Q-tensor model of liquid crystals. Though present in the original derivation of the Ericksen-Leslie equations for nematic liquid crystals, the inertia term of the…

Numerical Analysis · Mathematics 2024-10-25 Max Hirsch , Franziska Weber , Yukun Yue

We perform exact Statistical Mechanics calculations for a system of elongated objects (hard needles) that are restricted to translate along a line and rotate within a plane, and that interact via both excluded-volume steric repulsion and…

Statistical Mechanics · Physics 2023-04-11 Danilo B. Liarte , Alberto Petri , Silvio R. Salinas

We consider the physical setup of a three-dimensional fluid-structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by a hyperbolic…

Analysis of PDEs · Mathematics 2021-08-09 Dominic Breit , Malte Kampschulte , Sebastian Schwarzacher

We propose a fluid-rigid body interaction benchmark problem, consisting of a solid spherical obstacle in a Newtonian fluid, whose centre of mass is fixed but is free to rotate. A number of different problems are defined for both two and…

Computational Physics · Physics 2019-09-20 Henry von Wahl , Thomas Richter , Christoph Lehrenfeld , Jan Heiland , Piotr Minakowski

In this paper, we study the long-time behavior of full Ericksen-Leslie system modeling the hydrodynamics of nematic liquid crystals between two dimensional unit spheres. Under a weaker assumption for Leslie's coefficients, we give the key…

Analysis of PDEs · Mathematics 2023-02-24 Tao Huang , Chengyuan Qu

The Ericksen-Leslie model for nematic liquid crystal flows in case of an isothermal and incompressible fluid with general Leslie stress and anisotropic elasticity, i.e. with general Ericksen stress tensor, is shown for the first time to be…

Analysis of PDEs · Mathematics 2025-11-25 Matthias Hieber , Jinkai Li , Mathias Wilke

In this paper we consider the 3D co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in a thin strip. The system contains the incompressible Navier-Stokes, coupled with a parabolic system for…

Analysis of PDEs · Mathematics 2024-11-15 Francesco De Anna , Xingyu Li , Marius Paicu , Arghir Zarnescu

We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…

Analysis of PDEs · Mathematics 2015-05-14 Marius Paicu , Arghir Zarnescu

We study the growth of aligned domains in nematic liquid crystals. Results are obtained solving the Beris-Edwards equations of motion using the lattice Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a consequence…

Soft Condensed Matter · Physics 2007-05-23 Geza Toth , Colin Denniston , J. M. Yeomans

In this article, we study the new Q-tensor model previously derived from Onsager's molecular theory by Han \textit{et al.} [Arch. Rational Mech. Anal., 215.3 (2014), pp. 741-809] for static liquid crystal modeling. Taking density and…

Soft Condensed Matter · Physics 2015-06-16 Song Mei , Pingwen Zhang

We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity…

Analysis of PDEs · Mathematics 2022-02-23 Robert Denk , Jürgen Saal