Uniform convergence to the equilibrium of the homogeneous Boltzmann-Fermi-Dirac Equation with moderately soft potential

2025/04/02 by Jiang, Ning, Wang, Chenchen
#35B40 #35Q20 #76P05 #82C40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.01341

Abstract

We concern the long-time behavior of mild solutions to the spatially homogeneous Boltzmann--Fermi--Dirac equation with moderately soft potential. Based on the well-posedness results in [X-G. Lu, J. Stat. Phys., 105, (2001), 353-388], we prove that the mild solution decays algebraically to the Fermi--Dirac statistics with an explicit rate. Under the framework of the level set analysis by De Giorgi, we derive an L^∞ estimate which is uniform with respect to the quantum parameter ε. All quantitative estimates are independent of ε, which implies that they also hold in the classical limit, i.e., the Boltzmann equation.

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