  We study the global existence of weak solutions to a multi-dimensional
simplified Ericksen-Leslie system for compressible flows of nematic liquid
crystals with large initial energy in a bounded domain $\Omega\subset
\mathbb{R}^N$, where N=2 or 3. By exploiting a maximum principle, Nirenberg's
interpolation inequality and a smallness condition imposed on the $N$-th
component of initial direction field $\mf{d}_0$ to overcome the difficulties
induced by the supercritical nonlinearity $|\nabla{\mathbf d}|^2{\mathbf d}$ in
the equations of angular momentum, and then adapting a modified
three-dimensional approximation scheme and the weak convergence arguments for
the compressible Navier-Stokes equations, we establish the global existence of
weak solutions to the initial-boundary problem with large initial energy and
without any smallness condition on the initial density and velocity.
