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

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Date
2007
Link to item file
http://hal.archives-ouvertes.fr/hal-00079949/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
uniform in time; regularity bounds; mo- ment bounds; soft potentials; spatially homogeneous; Boltzmann equation
Journal issue
Asymptotic Analysis
Volume
54
Number
3-4
Publication date
2007
Article pages
235-245
Publisher
Amsterdam : IOS Press
URI
https://basepub.dauphine.fr/handle/123456789/391
Collections
  • CEREMADE : Publications
Metadata
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Author
Desvillettes, Laurent
Mouhot, Clément
Type
Article accepté pour publication ou publié
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]).

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