Contents Online
Communications in Mathematical Sciences
Volume 20 (2022)
Number 8
Rarefied gas dynamics with external fields under specular reflection boundary condition
Pages: 2133 – 2206
DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n8.a3
Author
Abstract
We consider the Boltzmann equation with external fields in strictly convex domains with the specular reflection boundary condition. We construct classical $C^1$ solutions away from the grazing set under the assumption that the external field is $C^1$ and the normal derivative of the field is positive and bounded away from zero.
Keywords
Boltzmann, boundary, specular, regularity, field
2010 Mathematics Subject Classification
35B65, 35Q20, 82B40
Received 25 December 2020
Received revised 21 August 2021
Accepted 25 February 2022
Published 29 November 2022