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Short time existence of classical solutions is proved for a system ofequations that involves a three excitations kinetic operator. The system isrelated to the description of a gas of bosons below but close to the criticaltemperature, where the three excitations integral aims at describing theinteraction between the particles in the condensate and the excitations in thenormal gas. Some qualitative properties of the solutions are obtained.

Local classical solutions of a three excitations kinetic system for a homogeneous condensed gas of bosons