  We consider the complete system of equations governing the motion of a
general compressible, viscous, electrically and heat conductive fluid driven by
non-conservative boundary conditions. We show the existence of a bounded
absorbing set in the energy space and asymptotic compactness of trajectories.
As a corollary, the set of all entire globally bounded solutions is identified
as a natural attractor. Examples of boundary conditions giving rise to
unbounded solutions are also discussed.
