Stability estimates of the Boltzmann equation in a half space

Chae, Myeongju; Ha, Seung-Yeal

doi:10.1090/S0033-569X-07-01060-4

Authors: Myeongju Chae and Seung-Yeal Ha
Journal: Quart. Appl. Math. 65 (2007), 653-682
MSC (2000): Primary 35Q35
DOI: https://doi.org/10.1090/S0033-569X-07-01060-4
Published electronically: August 24, 2007
MathSciNet review: 2370355
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Abstract: In this paper, we study the large-time behavior and the stability of continuous mild solutions to the Boltzmann equation in a half space. For this, we introduce two nonlinear functionals measuring future binary collisions and $L^1$-distance. Through the time-decay estimates of these functionals and the pointwise estimate of the gain part of the collision operator, we show that continuous mild solutions approach to collision free flows time-asymptotically in $L^1$, and $L^1$-distance at time $t$ is uniformly bounded by that of corresponding initial data, when initial datum is a small perturbation of the vacuum.

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