On the speed of approach to equilibrium for a collisionless gas

2010/09/15 by Kazuo Aoki, François Golse · 26 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Distribution (mathematics) #Gas Dynamics and Kinetic Theory #Maxwell–Boltzmann distribution #Quantum Electrodynamics and Casimir Effect #Reflection (computer programming) #Thermalisation #Thermodynamic equilibrium #math-ph #math.AP #math.MP #msc:82C40

paper · pdf · doi:10.3934/krm.2011.4.87

published in Kinetic and Related Models 4(1), 87-107 (American Institute of Mathematical Sciences) · 22 pages, 1 figure; submitted to Kinetic and Related Models

arxiv created 2010/09/15 · openalex publication_date 2011/01/01 · arxiv updated 2012/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform,constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We establish lower bounds for potential decay ratesassuming uniform L^p bounds on the initial distribution function. We also obtain a decay estimate in the spherically symmetric case. Wediscuss with particular care the influence of low-speed particles on thermalization by the wall.

Citations

• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
• Cercignani's Conjecture is Sometimes True and Always Almost True
• Hypocoercivity