Communications in Mathematical Sciences

Volume 20 (2022)

Number 8

Rarefied gas dynamics with external fields under specular reflection boundary condition

Pages: 2133 – 2206



Yunbai Cao (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.)


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.


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