Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions - Archive ouverte HAL Access content directly
Journal Articles Communications on Pure and Applied Analysis Year : 2020

Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions

Abstract

We consider the Boltzmann operator for mixtures with cutoff Maxwellian, hard potentials, or hard spheres collision kernels. In a perturbative regime around the global Maxwellian equilibrium, the linearized Boltzmann multi-species operator L is known to possess an explicit spectral gap λ , in the global equilibrium weighted L^2 space. We study a new operator L_ε obtained by linearizing the Boltzmann operator for mixtures around local Maxwellian distributions, where all the species evolve with different small macroscopic velocities of order ε, ε > 0. This is a non-equilibrium state for the mixture. We establish a quasi-stability property for the Dirichlet form of L_ε in the global equilibrium weighted L^2 space. More precisely, we consider the explicit upper bound that has been proved for the entropy production functional associated to L and we show that the same estimate holds for the entropy production functional associated to L_ε , up to a correction of order ε.
Fichier principal
Vignette du fichier
Stability_Spectral_Gap_Boltzmann.pdf (515.6 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01924308 , version 1 (15-11-2018)

Identifiers

Cite

Andrea Bondesan, Laurent Boudin, Marc Briant, Bérénice Grec. Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions. Communications on Pure and Applied Analysis, 2020, 19 (5), pp.2549-2573. ⟨10.3934/cpaa.2020112⟩. ⟨hal-01924308⟩
231 View
252 Download

Altmetric

Share

Gmail Facebook X LinkedIn More