A COUPLING APPROACH FOR THE CONVERGENCE TO EQUILIBRIUM FOR A COLLISIONLESS GAS

• 成果类型: Article
• 署名作者: Bernou, Armand; Fournier, Nicolas
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1696
• 发表日期: 2022
• 页码: 764-811
• 关键词: long-time behavior; BOUNDARY; semigroup; billiards; speed; rates

摘要

We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine, in total variation distance, the polynomial rate of convergence given in (Kinet. Relat. Models 4 (2011) 87-107) and (Comm. Math. Phys. 318 (2013) 375-409). This is, to our knowledge, the first quantitative result in collisionless kinetic theory in dimension equal to or larger than 2 that does not require any symmetry of the domain, nor a monokinetic regime. Our study is also more general in terms of reflection at the boundary: we allow for rather general diffusive reflections and for a specular reflection component.