相关论文: Interaction of liquid crystals with a rigid body
We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the…
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…
We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations. We prove the global existence of classical solution with…
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…
In this paper, we prove the existence and uniqueness of local strong solutions of the hydrodynamics of nematic liquid crystals system under the initial data satisfying a natural compatibility condition. Also the global strong solutions of…
In this article, the fluid-rigid body interaction problem of nematic liquid crystals described by the general Beris-Edwards $Q$-tensor model is studied. It is proved first that the total energy of this problem decreases in time. The…
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.
Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…
We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…
In this paper we establish the uniformity property of a simplified Ericksen-Leslie system modelling the hydrodynamics of nematic liquid crystals on the two dimensional unit sphere $S^2$, namely the uniform convergence in $L^2$ to a steady…
The work deals with the Ericksen-Leslie model for nematic liquid crystals on the whole space, the half-space and on exterior domains with smooth boundary. The crystal orientation is described by a unit vector that is a small perturbation of…
The work deals with the Ericksen-Leslie System for nematic liquid crystals on the whole space. In our work we suppose the initial condition of the orientation field stays on an arc connecting two fixed orthogonal vectors on the unit sphere.…
In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie…
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…
We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in $\mathbb R^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we…
This paper establishes the global well-posedness and long-time dynamics of the general Ericksen--Leslie system for isotropic nematic liquid crystals under a constant magnetic field. On the two-dimensional torus $\mathbb{T}^2$, a liquid…
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…
In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies…