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

Bose condensate inb interaction with excitations - a two-component space-dependent model close to equilibrium