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 production 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, convergence, some results on the long-time bt behavior of the conservative isotropic solutions of the BBE equation are obtained, including the velocity concentration at very low temperatures and the tendency toward equilibrium states at very high temperatures.