Communications in Mathematical Sciences

Volume 15 (2017)

Number 8

Uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows

Pages: 2219 – 2278

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n8.a6

Authors

Jincheng Gao (School of Mathematics, Sun Yat-sen University, Guangzhou, China)

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Yaqing Liu (School of Applied Science, Beijing Information Science and Technology University, Beijing, China)

Abstract

In this paper, we study the uniform regularity and vanishing viscosity limit for the compressible nematic liquid crystal flows in three-dimensional bounded domains. One establishes the uniform estimates for the solutions in a conormal Sobolev space and obtains the uniform estimates for the density and velocity in $W^{1,\infty}$. Then, it is shown that there exists a unique strong solution for the compressible nematic liquid crystal flows in a finite time interval which is independent of the viscosity coefficient. Based on the uniform estimates, we also obtain the convergence rate of the viscous solutions to the inviscid ones with a rate of convergence.

Keywords

nematic liquid crystal flows, vanishing viscosity limit, conormal sobolev space, convergence rate

2010 Mathematics Subject Classification

35B65, 35Q35, 76N10

Full Text (PDF format)

Jincheng Gao’s research was partially supported by Guangdong Natural Science Foundation (Grant No.2014A030313161), China Postdoctoral Science Foundation Project (Grant No.2016M600064 and No.2017T100053), and NNSF of China(Grant No.11571380). Boling Guo’s research was partially supported by the NNSF of China(Grants No.11731014).

Received 29 November 2016

Accepted 23 August 2017

Published 20 December 2017