Abstract
This paper studies the boundedness of solutionsf of the initial-value problem for the space-homogeneous Boltzmann equation for inverse kth power forces, whenk>5, and under angular cutoff. The main result is that if the initial value isf 0 ⩾ 0 with (1 + ¦υ¦2)φ0 εL 1 and (1 + ¦υ¦)s f 0ε L∞ for somes > 2, then (1 + ¦υ¦s'f tεL ∞ fort>0 and essυ,t sup(1 + ¦υ¦)s'f(υ, t,) < ∞ for anys′ ⩽ s whens ⩽ 5, and anys′ ⩽ s ifs > 5.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
L. Arkeryd, On the Boltzmann equation,Arch. Rat. Mechs. Anal. 45:1–34 (1972).
T. Carleman,Problèmes mathématiques dans la théorie cinétique des gaz (Almqvist and Wiksell, Uppsala, 1957).
T. Elmroth, Global boundedness of moments of solutions of the Boltzmann equation for infinite range forces, to appear inArch. Rat. Mechs. Anal. (1983).
C. Truesdell and R. G. Muncaster,Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic Press, New York, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Arkeryd, L. L ∞ estimates for the space-homogeneous Boltzmann equation. J Stat Phys 31, 347–361 (1983). https://doi.org/10.1007/BF01011586
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01011586