  The linearization around one of its equilibrium of a system that describes
the correlations between the superfluid component and the normal fluid part of
a condensed Bose gas in the approximation of very low temperature and small
condensate density, is studied. A simple and transparent argument gives a
necessary and sufficient condition on the initial data for the existence of
global solutions satisfying the conservation of the total number of particles
and energy. Their convergence to a suitable stationary state is also shown and
rates of convergence for the normal fluid and superfluid components are
obtained.
