  This paper is devoted to the full system of incompressible liquid crystals,
as modeled in the Q-tensor framework. The main purpose is to establish the
uniqueness of weak solutions in a two dimensional setting, without imposing an
extra regularity on the solutions themselves. This result only requires the
initial data to fulfill the features which allow the existence of a weak
solution. Thus, we also present a revisit of the global existence result in
dimension two and three.
