相关论文: Regularity of Solutions to the Liquid Crystals Sys…

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…

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…

In this paper we study the large time behavior of solutions to a nematic liquid crystals system in the whole space $\mathbb{R}^3$. The fluid under consideration has constant density and small initial data.

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 here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the…

In this paper, we prove the global existence of weak solutions to the non-isothermal nematic liquid crystal system on $\mathbb T^2$, based on a new approximate system which is different from the classical Ginzburg-Landau approximation.…

We consider the strong and weak solutions to the Cauchy problem of the inhomogeneous incompressible nematic liquid crystal equations in two dimensions. We first establish the local existence and uniqueness of strong solutions by using the…

This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…

We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$.

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in…

In this paper, we establish an $\epsilon$-regularity criterion for any weak solution $(u,d)$ to the nematic liquid crystal flow (1.1) such that $(u,\nabla d)\in L^p_tL^q_x$ for some $p\ge 2$ and $q\ge n$ satisfying the condition (1.2). As…

In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows in $n(n=2$ or $3)$ dimensional bounded domain. More precisely, we obtain the local existence and uniqueness of the solutions when the viscosity…

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…

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…

In this paper, we study the Cauchy problem to the density-dependent liquid crystal system in $\mathbb R^3$. We establish the local existence and uniqueness of strong solutions to this system. In order to overcome the difficulties caused by…

In this paper, we study the active hydrodynamics, described in the Q-tensor liquid crystal framework. We prove the existence of global weak solutions in dimension two and three, with suitable initial datas. By using Littlewood-Paley…

In this paper, we consider the Dirichlet problem of inhomogeneous incompressible nematic liquid crystal equations in bounded smooth domains of two or three dimensions. We prove the global existence and uniqueness of strong solutions with…

In this paper, we mainly study a hydrodynamic system modeling the flow of nematic liquid crystals. In three dimensions, we first establish local well-posedness of the initial-boundary value problem of the system. Then, we prove the…

We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly…

In this paper, we investigate the uniform regularity and vanishing limit for the incompressible nematic liquid crystal flows in three dimensional bounded domain. It is shown that there exists a unique strong solution for the incompressible…