On the Boltzmann-Fermi-Dirac Equation for Hard Potential: Global Existence and Uniqueness, Gaussian Lower Bound, and Moment Estimates

2025/11/04 by Gayoung An, An, Gayoung, Sungbin Park +1
Mathematics · #35Q20 #35Q40 #82C40 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2511.02273

openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the global existence and uniqueness, Gaussian lower bound, and moment estimates in the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for hard potential (0≤ γ≤ 2) with angular cutoff b. Our results extend classical results to the Boltzmann-Fermi-Dirac setting. In detail, (1) we show existence, uniqueness, and L¹₂ stability of global-in-time solutions of the Boltzmann-Fermi-Dirac equation. (2) Assuming the solution is not a saturated equilibrium, we prove creation of a Gaussian lower bound for the solution. (3) We prove creation and propagation of L¹ polynomial and exponential moments of the solution under additional assumptions on the angular kernel b and 0<γ≤ 2. (4) Finally, we show propagation of L^∞ Gaussian and polynomial upper bounds when b is constant and 0<γ≤ 1.

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