On the Convergence to Equilibrium for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision kernel includes the Coulomb potential with a weaker angular cutoff. The proof is based on moment estimates, entropy dissipation inequalities, regularity of the collision gain operator, and a new observation that many collision kernels are larger than or equal to some completely positive kernels, which enables us to avoid dealing with the convergence problem of the cubic collision integrals.

Automated summary

In this paper, we prove the strong and time-averaged strong convergence to equilibrium for solutions of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles with general initial data. The assumption on the collision kernel includes the Coulomb potential with a weaker angular cutoff. The proof is based on moment estimates, entropy dissipation inequalities, regularity of the collision gain operator, and a new observation regarding the comparison of collision kernels.