Global Existence and Regularity for the Full Coupled Navier–Stokes and<i>Q</i>-Tensor System

Abstract

In this paper we study the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. Under certain conditions we prove the global existence of weak solutions in dimension two or three and the existence of global regular solutions in dimension two. We also prove the weak-strong uniqueness of the solutions, for sufficiently regular initial data.