Incompressible Limit of a Compressible Liquid Crystals System

TL;DR

This paper investigates the behavior of solutions to the compressible liquid crystals system as they approach the incompressible limit, considering both unbounded and bounded domains in two and three dimensions.

Contribution

It provides a rigorous analysis of the incompressible limit for the compressible liquid crystals system in various domain settings and dimensions.

Findings

Established convergence to incompressible system

Analyzed effects of domain boundary conditions

Extended results to 2D and 3D cases

Abstract

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space $\mathbb{R}^{\mathbb{N}}$ and a bounded domain of $\mathbb{R}^{\mathbb{N}}$ with Dirichlet boundary conditions. Here the number of dimension $\mathbb{N}=2$ or 3.