Incompressible Limit of the Compressible Nematic Liquid Crystal Flow

TL;DR

This paper rigorously proves that solutions of the compressible nematic liquid crystal flow converge to those of the incompressible flow as the Mach number approaches zero, including convergence rates.

Contribution

It establishes the incompressible limit for the compressible nematic liquid crystal flow with convergence rates, extending previous results to this specific system.

Findings

Strong solutions of compressible flow converge to incompressible solutions

Convergence rates are quantitatively obtained

Results hold for both local and global solutions

Abstract

This paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in R^N(N = 2, 3). It is rigorously shown that the local (and global) strong solution of the compressible system converges to the local (and global) strong solution of the incompressible system. Furthermore, the convergence rates are also obtained in some sense.