Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials

Abstract

We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated with hard potentials interactions under angular cut-off assumption, providing an explicit – algebraic – rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of [15] and is based upon new uniform-in-time-and-ε $L^{\infty }$ bound on the solutions.