Global existence and stability of solutions of spatially homogeneous Boltzmann equation for Fermi-Dirac particles

This paper deals with the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard sphere model. Firstly, we prove the global existence and uniqueness of classical solutions to this problem and give the corresponding L infinity and L13 estimates of solutions. To achieve this aim, we give the global existence of an intermediate equation which behaves as classical Boltzmann equation, then we prove that the intermediate solutions become the original solutions when the L infinity-bound of intermediate solutions less than a fixed constant. Then using the uniformly bounded L13 estimation, we prove the stability of spatially homogeneous Boltzmann equation for Fermi-Dirac particles. In addition, an upper bound of L13 estimate of classical Boltzmann equation at infinite time interval is given. Using this useful estimate we prove the stability between quantum Boltzmann equation and classical Boltzmann equation when the Planck constant tends to zero.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the spatially homogeneous Boltzmann equation for Fermi-Dirac particles in the hard sphere model. The global existence and uniqueness of classical solutions to this problem are proven, along with the corresponding L infinity and L13 estimates of the solutions. The stability of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles is demonstrated using uniformly bounded L13 estimation. Additionally, an upper bound of L13 estimate for the classical Boltzmann equation at infinite time interval is provided. The stability between the quantum Boltzmann equation and the classical Boltzmann equation as the Planck constant tends to zero is also proven.