Communications in Mathematical Sciences

Volume 19 (2021)

Number 5

Existence of global weak solutions to the compressible Ericksen–Leslie system in dimension one

Pages: 1269 – 1300

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n5.a5

Authors

Huajun Gong (College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong, China)

Tao Huang (Department of Mathematics, Wayne State University, Detroit, Michigan, U.S.A.)

Changyou Wang (Department of Mathematics, Purdue University, West Lafayette, Indiana, U.S.A.)

Abstract

We consider the compressible Ericksen–Leslie system of liquid crystal flows in one dimension. A global weak solution is constructed with initial density $\rho_0 \geq 0$ and $\rho_0 \in L^\gamma$ for $\gamma \gt 1$.

Keywords

compressible Ericksen–Leslie system, weak solution, nematic liquid crystals

2010 Mathematics Subject Classification

35Dxx, 35K55

The first-named author is supported in part by the National Natural Science Foundation of China grants 11601342, 11871345, and 61872429.

The third-named author is partially supported by NSF DMS 1764417.

Received 16 June 2020

Accepted 3 January 2021

Published 7 July 2021