Communications in Mathematical Sciences
Volume 13 (2015)
Global weak solution for a coupled compressible Navier-Stokes and $Q$-tensor system
Pages: 49 – 82
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