In this paper, we review some recent results on the Boltzmann equation near the equilibrium states in the whole space $\mathbb R^n$. The emphasize is put on the well-posedness of the solution in some Sobolev space without time derivatives and its uniform stability and optimal decay rates, and also on the existence and asymptotical stability of the time-periodic solution. Most of results obtained here are proved by combining the energy estimates and the spectral analysis.
Publié le : 2007-09-15
Classification:
Boltzmann equation,
equilibrium state,
energy estimates,
76P05,
82C40,
82D05
@article{1224877825,
author = {Duan, Renjun},
title = {The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$},
journal = {Methods Appl. Anal.},
volume = {14},
number = {1},
year = {2007},
pages = { 227-250},
language = {en},
url = {http://dml.mathdoc.fr/item/1224877825}
}
Duan, Renjun. The Boltzmann Equation Near Equilibrium States in $\mathbb R^n$. Methods Appl. Anal., Tome 14 (2007) no. 1, pp. 227-250. http://gdmltest.u-ga.fr/item/1224877825/