相关论文: Nematic Liquid Crystals in Lipschitz domains

In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small…

We study a modified Landau-de Gennes model for nematic liquid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional domains,…

For suitable initial and boundary data, we construct infinitely many weak solutions to the nematic liquid crystal flows in dimension three. These solutions are in the axisymmetric class with bounded energy and backward bubbling at a large…

The free boundary problem for a two-dimensional fluid filtered in porous media is studied. This is known as the one-phase Muskat problem and is mathematically equivalent to the vertical Hele-Shaw problem driven by gravity force. We prove…

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the…

We study the well-posedness of the Cauchy problem with Dirichlet or Neumann boundary conditions associated to an H 1 -critical semilinear wave equation on a smooth bounded 2D domain {\Omega}. First, we prove an appropriate Strichartz type…

In this article, we consider 2D second grade fluid equations in exterior domain with Dirichlet boundary conditions. For initial data $\boldsymbol{u}_0 \in \boldsymbol{H}^3(\Omega)$, the system is shown to be global well-posed. Furthermore,…

We consider Maxwell equations on a smooth domain with perfectly conducting boundary conditions in isotropic media in two and three dimensions. In the charge-free case we recover Strichartz estimates due to Blair--Smith--Sogge for wave…

We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in $H^s, s>\frac{d}{2}+1$, the…

We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic…

The critical field of the Freedericksz transition and switching dynamics are investigated for polymer stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the…

We consider here the simplified Ericksen-Leslie system on the whole three-dimensional space. This system deals with the incompressible Navier-Stokes equations strongly coupled with a harmonic map flow which models the dynamical behavior for…

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…

We study the weak anchoring condition for nematic liquid crystals in the context of the Landau-De Gennes model. We restrict our attention to two dimensional samples and to nematic director fields lying in the plane, for which the Landau-De…

We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent with the…

In this paper, we establish the well-posedness in energy space for the quintic energy critical wave inside a cylindrical convex domain $\Omega\subset\mathbb{R}^3$ with smooth boundary $\partial\Omega\neq\emptyset$. The key tools to prove…

In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This system of SPDEs is also known as the stochastic…

In this paper, we consider the boundary value problem of a simplified Ericksen-Leslie system in dimension two with non-slip boundary condition for the velocity field $u$ and time-dependent boundary condition for the director field $d$ of…

The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves leveraging differentiability properties of the…

The improved expansion in width is applied to curved domain walls in uniaxial nematic liquid crystals in external magnetic field. In the present paper we concentrate on the case of equal elastic constants. We obtain approximate form of the…