  The paper considers a model for Bose gases in the so-called 'high-temperature
range' below the temperature Tc, where Bose-Einstein condensation sets in.The
model is of non-linear two-component type, consisting of a kinetic equation
with periodic boundary conditions for the distribution function of a gas of
excitations interacting with a Bose condensate, which is described by a
Gross-Pitaevskii equation. Results on well-posedness and long time behaviour
are proved in a H1-setting close to equilibrium.
