Related papers: Global minimisers of cholesteric liquid crystal sy…
We study the global (asymptotic) stability of the Lengyel-Epstein differential systems, sometimes called Belousov-Zhabotinsky differential systems. Such systems are topologically equivalent to a two-parameter family of cubic systems in the…
In this work, we revisit the study by M. E. Schonbek [11] concerning the problem of existence of global entropic weak solutions for the classical Boussinesq system, as well as the study of the regularity of these solutions by C. J. Amick…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space…
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 $\gamma>1$.
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…
In this article, we consider the Ericksen-Leslie's hyperbolic system for compressible liquid crystal model in three spatial dimensions. Global regularity for small and smooth initial data near equilibrium is proved for the case that the…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…
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 deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion \begin{equation}\nonumber \left\{ \begin{aligned} &n_t+u\cdot\nabla…
We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to…
In this paper, we study minimizers of the Chon\'e--Rochet variational problem in dimension two. We first establish global $C^1$ regularity on arbitrary bounded convex domains, and then prove global $C^{1,1}$ regularity on bounded strictly…
We prove the first convergence guarantees for a subgradient method minimizing a generic Lipschitz function over generic Lipschitz inequality constraints. No smoothness or convexity (or weak convexity) assumptions are made. Instead, we…
We study the hydrodynamics of compressible flows of active liquid crystals in the Beris-Edwards hydrodynamics framework, using the Landau-de Gennes $Q$-tensor order parameter to describe liquid crystalline ordering. We prove the existence…
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a corresponding physically…
We consider a two-dimensional nonlinear Schr{\"o}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both…
We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau-de Gennes model. The nematic is assumed to occupy the exterior of a ball of radius r_0, satisfy…
The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not…
We study uniaxial energy minimizers within the Landau-de Gennes theory for nematic liquid crystals, subject to dirichlet boundary conditions. Topological defects in such minimizers correspond to the zeros of the corresponding equilibrium…