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



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.)


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.


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

2010 Mathematics Subject Classification

35A01, 35A02, 76A10, 76D03

Published 16 July 2014