Interior regularity criterion for incompressible Ericksen-Leslie system

Well-posedness of the Ericksen-leslie System

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 system is dissipated. Instead of the GinzburgLandau approximation, we construct an approximate system with the dissipated energy based on a new formulation of th...

Regularity and Existence of Global Solutions to the Ericksen-leslie System in R

In this paper, we first establish the regularity theorem for suitable weak solutions to the EricksenLeslie system in R2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen-Leslie system in R2 for any initial data in the energy space, under the physical constraint conditions on the Leslie coefficients ensuring the dissipation of energy of the...

A fundamental improvement to Ericksen-Leslie kinematics

We demonstrate theory and computations for finite-energy line defect solutions in an improvement of Ericksen-Leslie liquid crystal theory. Planar director fields are considered in two and three space dimensions, and we demonstrate straight as well as loop disclination solutions. The possibility of static balance of forces in the presence of a disclination and in the absence of flow and body for...

Finite Difference Scheme for the Ericksen-leslie Equation

Ericksen Leslie equation describes the time evolution of a spin vector and velocity in liquid crystals. This equation has following property: (i) the length preserving of a spin vector, (ii) the energy conservation or the dissipation property, (iii) the incompressibility of a velocity vector. In physics papers, the fourth order Runge-Kutta’s method is used for numerical analysis of some types o...

A Regularity Criterion for the 3D Incompressible Density-Dependent Navier-Stokes-Allen-Cahn Equations