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- Title
Cercignani-Lampis boundary in the Boltzmann theory.
- Authors
Chen, Hongxu
- Abstract
The Boltzmann equation is a fundamental kinetic equation that describes the dynamics of dilute gas. In this paper we study the local well-posedness of the Boltzmann equation in bounded domain with the Cercignani-Lampis boundary condition, which describes the intermediate reflection law between diffuse reflection and specular reflection via two accommodation coefficients. We prove the local-in-time well-posedness of the equation by establishing an L∞ estimate. In particular, for the L∞ bound we develop a new decomposition on the boundary term combining with repeated interaction through the characteristic. Moreover, under some constraints on the wall temperature and the accommodation coefficients, we construct a unique steady solution of the Boltzmann equation.
- Subjects
GAS dynamics; BOUNDARY value problems
- Publication
Kinetic & Related Models, 2020, Vol 13, Issue 3, p549
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2020019