Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
Mouhot, Clément (2006), Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials, Communications in Mathematical Physics, 261, p. 629-672. http://dx.doi.org/10.1007/s00220-005-1455-x
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00076709/en/
Journal nameCommunications in Mathematical Physics
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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.
Subjects / KeywordsBoltzmann equation; entropy production; rate of convergence; trend to equilibrium; explicit; spectral gap; spectrum; linearized Boltzmann collision operator; spatially homogeneous
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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) Article accepté pour publication ou publié