On multi-dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain

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 of 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 d(0) to overcome the difficulties induced by the supercritical nonlinearity vertical bar del d vertical bar(2)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. (C) 2013 Elsevier Inc. All rights reserved.