Quantitative lower bound for solutions to the Boltzmann equation in non-convex domains

2025/05/06 by Jhe-Kuan Su, Su, Jhe-Kuan
Computer Science · Engineering · Mathematics · #35Q20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2505.03396

openalex publication_date 2025/05/06 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a Maxwellian lower bound in the cutoff case, and a weaker-than-Maxwellian lower bound for the non-cutoff case. This extends the results of \citeBri1,Bri2, where the convexity of the domain was required.

Related

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• Conditional appearance of decay for the non-cutoff Boltzmann equation in a bounded domain
• Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian
• Bounded Solutions of the Boltzmann Equation in the Whole Space
• The Non-cutoff Boltzmann Equation in Bounded Domains