A modified Boltzmann equation for Bose-Einstein particles: Isotropic solutions and long-time behavior

Under some strong cutoff conditions on collision kernels, global existence, local stability, entropy identity, conservation of energy, and moment prod uction estimates are proven for isotropic solutions of a modified (quantum effect) Boltzmann equation For spatially homogeneous gases of Pose Einstein particles (BBE). Then applying these results with the biting-weak, converg ence, some results on the long-time bt behavior of the conservative isotrop ic solutions of the BBE equation are obtained, including the velocity conce ntration at very low temperatures and the tendency toward equilibrium state s at very high temperatures.