Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three

Abstract

In this paper, we consider the initial and boundary value problem of a simplified compressible nematic liquid crystal flow in $\hat{I}\text{c◯}\subset {\mathbb{R}}^3$. We establish the existence of global weak solutions, provided the initial orientational director field $d_0$ lies in the hemisphere ${\mathbb{S}}_{+}^2$.

27 pages