  The general Ericksen-Leslie system for the flow of nematic liquid crystals is
reconsidered in the non-isothermal case aiming for thermodynamically consistent
models. The non-isothermal model is then investigated analytically. A fairly
complete dynamic theory is developed by analyzing these systems as quasilinear
parabolic evolution equations in an $L^p-L^q$-setting. First, the existence of
a unique, local strong solution is proved. It is then shown that 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 these cases, the solution converges exponentially to
an equilibrium in the natural state manifold.
