  We consider weak solutions to a two-dimensional simplified Ericksen-Leslie
system of compressible flow of nematic liquid crystals. An initial-boundary
value problem is first studied in a bounded domain. By developing new
techniques and estimates to overcome the difficulties induced by the
supercritical nonlinearity in the equations of angular momentum on the
direction field, and adapting the standard three-level approximation scheme and
the weak convergence arguments for the compressible Navier-Stokes equations, we
establish the global existence of weak solutions under a restriction imposed on
the initial energy including the case of small initial energy. Then the Cauchy
problem with large initial data is investigated, and we prove the global
existence of large weak solutions by using the domain expansion technique and
the rigidity theorem, provided that the second component of initial data of the
direction field satisfies some geometric angle condition.
