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Related papers: On a non-isothermal model for nematic liquid cryst…

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Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…

Analysis of PDEs · Mathematics 2013-02-20 Matthias Hieber , Manuel Nesensohn , Jan Prüss , Katharina Schade

We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…

Analysis of PDEs · Mathematics 2013-06-27 Xianpeng Hu , Hao Wu

For any smooth domain $\Omega\subset \mathbb{R}^3$, we establish the existence of a global weak solution $(\mathbf{u},\mathbf{d}, \theta)$ to the simplified, non-isothermal Ericksen-Leslie system modeling the hydrodynamic motion of nematic…

Analysis of PDEs · Mathematics 2020-01-07 Hengrong Du , Yimei Li , Changyou Wang

We study the evolution of phase-transition-generated cosmic magnetic fields coupled to the primeval cosmic plasma in turbulent and viscous free-streaming regimes. The evolution laws for the magnetic energy density and correlation length,…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-15 Leonardo Campanelli

In this paper we study a mathematical model describing the movement of a colloidal particle in a fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is governed by the Beris-Edwards…

Analysis of PDEs · Mathematics 2023-10-26 Zhiyuan Geng , Arnab Roy , ArghirZarnescu

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

We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter (related to different symmetries of the crystal lattice in the phase…

Analysis of PDEs · Mathematics 2013-07-08 Elena Bonetti , Pierluigi Colli , Mauro Fabrizio , Gianni Gilardi

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 consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an…

Analysis of PDEs · Mathematics 2007-05-23 Maurizio Grasselli , Hana Petzeltova , Giulio Schimperna

The stationary Navier-Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet type boundary conditions. The viscosity is supposed to depend on the temperature and the…

Analysis of PDEs · Mathematics 2025-01-27 Maurizio Grasselli , Nicola Parolini , Andrea Poiatti , Marco Verani

We consider the Navier-Stokes system describing motions of viscous compressible heat-conducting and "self-gravitating" media. We use the state function of the form $p(\eta,\theta)=p_0(\eta)+p_1(\eta)\theta$ linear with respect to the…

Mathematical Physics · Physics 2007-05-23 Bernard Ducomet , Alexander Zlotnik

We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three…

Analysis of PDEs · Mathematics 2026-05-19 Hengrong Du , Fizay-Noah Lee , Gieri Simonett

We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy…

Analysis of PDEs · Mathematics 2017-11-29 Ondrej Kreml , Vaclav Macha , Sarka Necasova , Aneta Wroblewska-Kaminska

We demonstrate that a first order isotropic-to-nematic phase transition in liquid crystals can be succesfully modeled within the generalized Landau-de Gennes theory by selecting an appropriate combination of elastic constants. The numerical…

Soft Condensed Matter · Physics 2019-02-19 Dmitry Golovaty , Young-Ki Kim , Oleg D. Lavrentovich , Michael Novack , Peter Sternberg

We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid…

Fluid Dynamics · Physics 2016-12-14 Alessio Bocci , Giovanni Mingari Scarpello , Daniele Ritelli

The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…

Numerical Analysis · Mathematics 2019-10-08 Craig S. MacDonald , John A. Mackenzie , Alison Ramage

We consider the initial boundary problem of 2D non-homogeneous incompressible heat conducting Navier-Stokes equations with vacuum, where the viscosity and heat conductivity depend on temperature in a power law of Chapman-Enskog. We derive…

Analysis of PDEs · Mathematics 2024-01-15 Wenchao Dong , Qingyan Li

We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence…

Analysis of PDEs · Mathematics 2026-01-06 Kuntal Bhandari , Apala Majumdar , Šárka Nečasová

In this work, we study the Cauchy problem of Poiseuille flow of the full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of two partial differential equations: One is a quasi-linear wave equation for the…

Analysis of PDEs · Mathematics 2023-09-06 Geng Chen , Weishi Liu , Majed Sofiani

The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proportional to the difference of the temperature inside and…

Analysis of PDEs · Mathematics 2015-11-23 Piotr B. Mucha , Milan Pokorný , Ewelina Zatorska