Decay of the Boltzmann Equation with the Specular Boundary Condition in Non-convex Cylindrical Domains
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SCOPUS
- Title
- Decay of the Boltzmann Equation with the Specular Boundary Condition in Non-convex Cylindrical Domains
- Authors
- KIM, CHANWOO; LEE, DONGHYUN
- Date Issued
- 2018-10
- Publisher
- SPRINGER
- Abstract
- The basic question about the existence, uniqueness, and stability of the Boltzmann equation in general non-convex domains with the specular reflection boundary condition has been widely open. In this paper, we consider cylindrical domains whose cross section is generally non-convex analytic bounded planar domain. We establish a global well-posedness and asymptotic stability of the Boltzmann equation with the specular reflection boundary condition. Our method consists of the delicate construction of -tubular neighborhoods of billiard trajectories which bounce infinitely many times or hit the boundary tangentially at some moment, and sharp estimates of the size of such neighborhoods.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/94493
- DOI
- 10.1007/s00205-018-1241-5
- ISSN
- 0003-9527
- Article Type
- Article
- Citation
- ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 230, no. 1, page. 49 - 123, 2018-10
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