Uniform Regularity and Vanishing Viscosity Limit for the Nematic Liquid Crystal Flows in Three Dimensional Domain

TL;DR

This paper establishes uniform regularity results and analyzes the vanishing viscosity limit for three-dimensional incompressible nematic liquid crystal flows, demonstrating existence, boundedness, and convergence properties independent of viscosity.

Contribution

It proves the existence of unique strong solutions with boundary conditions in 3D domains that are uniformly bounded and independent of viscosity, and studies their convergence to inviscid solutions.

Findings

Existence of unique strong solutions in finite time

Solutions are uniformly bounded in conormal Sobolev spaces

Convergence rate of viscous solutions to inviscid solutions analyzed

Abstract

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 nematic liquid crystal flows with boundary condition in a finite time interval which is independent of the viscosity. The solution is uniformly bounded in a conormal Sobolev space. Finally, we also study the convergence rate of the viscous solutions to the inviscid ones.