Regularity of the Boltzmann equation in convex domains

• 成果类型: Article
• 署名作者: Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane
• 署名单位: Brown University; University of Wisconsin System; University of Wisconsin Madison; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0670-8
• 发表日期: 2017
• 页码: 115-290
• 关键词: system

摘要

A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct solutions for and weighted solutions for as well.