Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials - Archive ouverte HAL Access content directly
Journal Articles Communications in Mathematical Physics Year : 2006

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

Abstract

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.
Fichier principal
Vignette du fichier
EEPTS-revi.pdf (471.39 Ko) Télécharger le fichier
Loading...

Dates and versions

hal-00076709 , version 1 (26-05-2006)
hal-00076709 , version 2 (26-05-2006)

Identifiers

Cite

Clément Mouhot. Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. Communications in Mathematical Physics, 2006, 261, pp.629-672. ⟨10.1007/s00220-005-1455-x⟩. ⟨hal-00076709v2⟩
313 View
251 Download

Altmetric

Share

Gmail Facebook X LinkedIn More