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Regularity of the Boltzmann equation in convex domains

Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane (2017), Regularity of the Boltzmann equation in convex domains, Inventiones Mathematicae, 207, 1, p. 115-290. 10.1007/s00222-016-0670-8

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1212.1694v4
Date
2017
Journal name
Inventiones Mathematicae
Volume
207
Number
1
Publisher
Springer
Pages
115-290
Publication identifier
Metadata
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Author(s)
Guo, Yan
Division of Applied Mathematics
Kim, Chanwoo

Tonon, Daniela
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Trescases, Ariane
Centre de Mathématiques et de Leurs Applications [CMLA]
Abstract (EN)
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 C1 solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct W1,p solutions for 1
Subjects / Keywords
Boltzmann