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In this note we prove the existence and uniqueness of local maximal smooth solution of the stochastic simplified Ericksen-Leslie systems modelling the dynamics of nematic liquid crystals under stochastic perturbations.

Analysis of PDEs · Mathematics 2020-11-03 Zdzislaw Brzezniak , Erika Hausenblas , Paul Razafimandimby

We consider the barotropic Navier--Stokes system describing the motion of a compressible Newtonian fluid in a bounded domain with in and out flux boundary conditions. We show that if the boundary velocity coincides with that of a rigid…

Analysis of PDEs · Mathematics 2020-05-06 Jan Brezina , Eduard Feireisl , Antonin Novotny

Interface between two phases of matter are ubiquitous in nature and technology. Determining the correct velocity condition at an interface is essential for understanding and designing of flows over a surface. We demonstrate that both the…

Fluid Dynamics · Physics 2016-08-31 Joseph John Thalakkottor , Kamran Mohseni

Active liquid crystals or active gels are soft materials which can be physically realised e.g. by preparing a solution of cytoskeletal filaments interacting with molecular motors. We study the hydrodynamics of an active liquid crystal in a…

Soft Condensed Matter · Physics 2007-06-29 D. Marenduzzo , E. Orlandini , M. E. Cates , J. M. Yeomans

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

We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…

Analysis of PDEs · Mathematics 2023-08-01 José M. Rodríguez , Raquel Taboada-Vázquez

We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain $\Omega \subset\mathbb R^3$. We first prove the local existence of unique strong solutions provided that the…

Analysis of PDEs · Mathematics 2016-11-25 Tao Huang , Changyou Wang , Huanyao Wen

In this paper we propose a time-splitting finite-element scheme for approximating solutions of the Ericksen-Leslie equations governing the flow of nematic liquid crystals. These equations are to be solved for a velocity vector field and a…

Numerical Analysis · Mathematics 2014-03-17 R. C. Cabrales , F. Guillén-González , J. V. Gutiérrez-Santacreu

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

In this paper, we consider numerical approximations for the model of smectic-A liquid crystal flows. The model equation, that is derived from the variational approach of the de Gennes free energy, is a highly nonlinear system that couples…

Numerical Analysis · Mathematics 2017-01-27 Xiaofeng Yang , Alex Brylev

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Dan Osborne , Zhongmin Qian

We consider a general family of regularized systems for the full Ericksen-Leslie model for the hydrodynamics of liquid crystals in $n$-dimensional compact Riemannian manifolds, $n$=2,3. The system we consider consists of a regularized…

Analysis of PDEs · Mathematics 2015-07-21 Ciprian G. Gal , Louis Tebou

We consider the Navier-Stokes-Fourier-Poisson system driven by an inhomogeneous temperature distribution on the boundary of an exterior fluid domain. We impose the finite mass constraint, positive far field condition for the temperature as…

Analysis of PDEs · Mathematics 2024-05-14 Nilasis Chaudhuri , Eduard Feireisl , Ewelina Zatorska , Boguslaw Zegarlinski

In this paper, we consider the initial and boundary value problem of Ericksen-Leslie system modeling nematic liquid crystal flows in dimension three. Two examples of singularity at finite time are constructed. The first example is…

Analysis of PDEs · Mathematics 2022-02-07 Tao Huang , Peiyong Wang

We use lattice Boltzmann simulations to solve the Beris-Edwards equations of motion for a cholesteric liquid crystal subjected to Poiseuille flow along the direction of the helical axis (permeative flow). The results allow us to clarify and…

Soft Condensed Matter · Physics 2009-11-10 D. Marenduzzo , E. Orlandini , J. M. Yeomans

In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid…

Analysis of PDEs · Mathematics 2012-11-27 Qing Chen , Zhong Tan , Guochun Wu

We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary…

Analysis of PDEs · Mathematics 2017-08-09 Maxim A. Olshanskii , Leo G. Rebholz , Abner J. Salgado

We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier--Stokes equations for the two-phase flow in the bulk, which are coupled to the transport…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

While the assumption of the ``no-slip" condition at a solid boundary is unquestioningly applied to study the flow characteristics of the Navier-Stokes fluid, there was considerable debate amongst the early pioneers of fluid mechanics, Du…

Fluid Dynamics · Physics 2023-10-31 Josef Málek , Kumbakonam R. Rajagopal

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field $\bm{u}$ when the system is segregated into two phases (at low temperatures) with a sharp interface between them. $\bm{u}$…

Statistical Mechanics · Physics 2016-08-31 Sorin Bastea , Raffaele Esposito , Joel L. Lebowitz , Rossana Marra