  Consider the (simplified) Leslie-Erickson model for the flow of nematic
liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$.
This article develops a complete dynamic theory for these equations, analyzing
the system as a quasilinear parabolic evolution equation in an
$L_p-L_q$-setting. First, the existence of a unique local strong solution is
proved. This solution extends to a global strong solution, provided the initial
data are close to an equilibrium or the solution is eventually bounded in the
natural norm of the underlying state space. In this case the solution converges
exponentially to an equilibrium. Moreover, the solution is shown to be real
analytic, jointly in time and space.
