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Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials

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Date
2006
Link to item file
http://hal.archives-ouvertes.fr/hal-00076709/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Boltzmann equation; entropy production; rate of convergence; trend to equilibrium; explicit; spectral gap; spectrum; linearized Boltzmann collision operator; spatially homogeneous
Journal issue
Communications in Mathematical Physics
Volume
261
Publication date
2006
Article pages
629-672
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00220-005-1455-x
URI
https://basepub.dauphine.fr/handle/123456789/711
Collections
  • CEREMADE : Publications
Metadata
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Author
Mouhot, Clément
Type
Article accepté pour publication ou publié
Abstract (EN)
For the spatially homogeneous Boltzmann equation with hard po- tentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, on which we provide a lower bound. Our approach is based on establishing spectral gap-like estimates valid near the equilibrium, and then connecting the latter to the quantitative nonlinear theory. This leads us to an explicit study of the linearized Boltzmann collision operator in functional spaces larger than the usual linearization setting.

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