Communications in Mathematical Sciences

Volume 13 (2015)

Number 1

Global weak solution for a coupled compressible Navier-Stokes and $Q$-tensor system

Pages: 49 – 82

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n1.a3

Authors

Dehua Wang (Department of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A.)

Xiang Xu (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A.)

Cheng Yu (Department of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A.)

Abstract

In this paper, we study a coupled compressible Navier-Stokes/$Q$-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence and long time dynamics of globally defined weak solutions for the coupled system are established, using weak convergence methods, compactness, and interpolation arguments. The symmetry and traceless properties of the $Q$-tensor play key roles in this process.

Keywords

Navier-Stokes, $Q$-tensor, liquid crystals, global weak solution, symmetric, traceless

2010 Mathematics Subject Classification

35A01, 35A02, 76A10, 76D03

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Published 16 July 2014