On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-dirac Particles

ABSTRACT. The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under the usual cut-off condition on the collision kernel, we prove a strong stability in L-topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L to equilibrium under a high temperature condition. The basic tools used are moment production estimates and the strong compactness of collision gain term.