Thumbnail - No thumbnail

Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials.

Desvillettes, Laurent; Mouhot, Clément (2007), Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials., Asymptotic Analysis, 54, 3-4, p. 235-245

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00079949/en/
Date
2007
Journal name
Asymptotic Analysis
Volume
54
Number
3-4
Publisher
Amsterdam : IOS Press
Pages
235-245
Metadata
Show full item record
Author(s)
Desvillettes, Laurent
Mouhot, Clément
Abstract (EN)
We consider the spatially homogeneous Boltzmann equation for regularized soft potentials and Grad's angular cutoff. We prove that uniform (in time) bounds in $L^1 ((1 + |v|^s)dv)$ and $H^k$ norms, $s, k \ge 0$ hold for its solution. The proof is based on the mixture of estimates of polynomial growth in time of those norms together with the quantitative results of relaxation to equilibrium in $L^1$ obtained by the so-called “entropy-entropy production” method in the context of dissipative systems with slowly growing a priori bounds (see reference [14]).
Subjects / Keywords
uniform in time; regularity bounds; mo- ment bounds; soft potentials; spatially homogeneous; Boltzmann equation