High-velocity tails of the inelastic and the multi-species mixture Boltzmann equations

2022/10/18 by Gayoung An, Donghyun Lee, An, Gayoung +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory

paper · pdf · doi:10.48550/arxiv.2210.09793

openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study high-velocity tails of some homogeneous Boltzmann equations on v ∈ ℝ_v^d. First, we consider spatially homogeneous inelastic Boltzmann equation with noncutoff collision kernel, in the case of moderately soft potentials. We also study spatially homogeneous mixture Boltzmann equations : for both noncutoff collision kernel with moderately soft potentials and cutoff collision kernel with hard potentials. In the case of noncutoff inelastic Boltzmann, we obtain f(t,v) ≥ a(t) e^-b(t)|v|p, 2 lt; p lt; 6.213 by extending Cancellation lemma and spreading lemma and assuming f∈ C^∞. For the Mixture type Boltzmann equations, we prove Maxwellian p=2.

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