2022/12/19 by Bocheng Liu, Liu, Bocheng, Xuguang Lu +1
Computer Science · Mathematics · #82C40 (35Q20) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2212.09287
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.