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Jang, Jinwoo
기하학 수리물리 연구단
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Propagation of Uniform Upper Bounds for the Spatially Homogeneous Relativistic Boltzmann Equation

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Title
Propagation of Uniform Upper Bounds for the Spatially Homogeneous Relativistic Boltzmann Equation
Author(s)
Jin Woo Jang; Robert M. Strain; Yun, Seok-Bae
Publication Date
2021-07
Journal
Archive for Rational Mechanics and Analysis, v.241, no.1, pp.149 - 186
Publisher
Springer Science and Business Media Deutschland GmbH
Abstract
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.In this paper, we prove the propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation. These polynomial and exponential L∞ bounds have been known to be a challenging open problem in relativistic kinetic theory. To accomplish this, we establish two types of estimates for the gain part of the collision operator. First, we prove a potential type estimate and a relativistic hyper-surface integral estimate. We then combine those estimates using the relativistic counterpart of the Carleman representation to derive uniform control of the gain term for the relativistic collision operator. This allows us to prove the desired propagation of the uniform bounds of the solution. We further present two applications of the propagation of the uniform upper bounds: another proof of the Boltzmann H-theorem, and the asymptotic convergence of solutions to the relativistic Maxwellian equilibrium.
URI
https://pr.ibs.re.kr/handle/8788114/9868
DOI
10.1007/s00205-021-01649-0
ISSN
0003-9527
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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