相关论文: On the uniqueness of weak solutions to the Erickse…
The Ericksen-Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows of nematic type. In this paper, we prove the uniqueness of global weak solutions to the general…
In this paper, we first establish the regularity theorem for suitable weak solutions to the Ericksen-Leslie system in dimensions two. Building on such a regularity, we then establish the existence of a global weak solution to the…
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…
Ericksen and Leslie established a theory to model the flow of nematic liquid crystals. This paper is devoted to the Cauchy Problem of a simplified version of their system, which retains most of the properties of the original one. We…
For any bounded smooth domain $\Omega\subset\mathbb R^3$, we establish the global existence of a weak solution $u:\Omega\times (0,+\infty)\to\mathbb R^3\times\mathbb S^2$ of the initial-boundary value (or the Cauchy) problem of the…
We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen--Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The…
For any bounded, smooth domain $\Omega\subset \R^2$, %(or $\Omega=\R^2$), we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of…
We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of…
In this paper, we consider the Cauchy problem to the Ericksen-Leslie system of liquid crystals in $\mathbb R^3$. Global well-posedness of strong solutions are obtained under the condition that the product of $\|u_0\|_2+\|\nabla d_0\|_2$ and…
We consider the compressible Ericksen-Leslie system of liquid crystal flows in one dimension. A global weak solution is constructed with initial density $\rho_0\geq 0$ and $\rho_0\in L^\gamma$ for $\gamma>1$.
We analyze the Ericksen-Leslie system equipped with the Oseen-Frank energy in three space dimensions. Recently, the author introduced the concept of measure-valued solutions to this system and showed the global existence of these…
We consider weak solutions to a two-dimensional simplified Ericksen-Leslie system of compressible flow of nematic liquid crystals. An initial-boundary value problem is first studied in a bounded domain. By developing new techniques and…
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 the first part of this paper, we establish global existence of solutions of the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The liquid crystal flow is a prototype of equations from the Ericksen-Leslie system in…
A quasistatic model due to Ericksen and Leslie describing incompressible liquid crystals is studied for a general class of free energies. Global existence of weak solutions is proven via a Galerkin approximation with eigenfunctions of a…
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…
In this paper, we study the Cauchy problem of the Poiseuille flow of full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of a parabolic equation for the velocity and a quasilinear wave equation for the…
We study the Ericksen-Leslie system equipped with a quadratic free energy functional. The norm restriction of the director is incorporated by a standard relaxation technique using a double-well potential. We use the relative energy concept,…
We investigate the Ericksen-Leslie system for the Oseen-Frank model with unequal Frank elastic constants in $\mathbb{R}^3$. To generalize the result of Hineman-Wang \cite{HW}, we prove existence of solutions to the Ericksen-Leslie system…
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…