  A nonlinear model due to Soddemann et al. [37] and Stewart [38] describing
incompressible smectic-A liquid crystals under flow is studied. In comparison
to previously considered models, this particular model takes into account
possible undulations of the layers away from equilibrium, which has been
observed in experiments. The emerging decoupling of the director and the layer
normal is incorporated by an additional evolution equation for the director.
Global existence of weak solutions to this model is proved via a Galerkin
approximation with eigenfunctions of the associated linear differential
operators in the three-dimensional case.
