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- Title
Regularity of Stationary Boltzmann Equation in Convex Domains.
- Authors
Chen, Hongxu; Kim, Chanwoo
- Abstract
The higher regularity estimate has been a challenging question regarding the Boltzmann equation in bounded domains. Indeed, it is well-known to have "the non-existence of a second order derivative at the boundary" in Guo et al. (Invent Math 207:115–290, 2017) even for symmetric convex domains such as a disk or sphere. In this paper, we answer this question in the affirmative by constructing the C 1 , β solutions away from the grazing boundary, for any β < 1 , to the stationary Boltzmann equation with the non-isothermal diffuse boundary condition in strictly convex domains, as long as a smooth wall temperature has small fluctuation pointwisely.
- Subjects
BOLTZMANN'S equation; SYMMETRIC domains; CONVEX domains; MATHEMATICS; GRAZING
- Publication
Archive for Rational Mechanics & Analysis, 2022, Vol 244, Issue 3, p1099
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-022-01781-5