A semigroup approach to the convergence rate of a collisionless gas - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

A semigroup approach to the convergence rate of a collisionless gas

Résumé

We study the rate of convergence to equilibrium for a collisionless (Knudsen) gas enclosed in a vessel in dimension n = 2 or 3. By semigroup arguments, we prove that in the L1 norm, the polynomial rate of convergence given in Tsuji, Aoki and Golse, 2010 and Kuo, Liu and Tsai, 2013 can be extended to any sufficiently regular domain, with standard assumptions on the inital data. This is to our knowledge, the first quantitative result in collisionless kinetic theory in dimension equal to or larger than 2 relying on deterministic arguments that does not require any symmetry of the domain, nor a monokinetic regime. The dependancy of the rate with respect to the initial distribution is detailed. We adress for the first time the case where the temperature at the boundary varies and the equilibrium distribution is no longer explicit. The demonstrations are adapted from a deterministic version of a subgeometric Harris' theorem recently established by Cañizo and Mischler, 2019. We also compare our model with a free-transport equation with absorbing boundary.
Fichier principal
Vignette du fichier
v5SemigroupAG.pdf (576.62 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02350998 , version 1 (06-11-2019)
hal-02350998 , version 2 (15-06-2020)

Identifiants

Citer

Armand Bernou. A semigroup approach to the convergence rate of a collisionless gas. 2019. ⟨hal-02350998v1⟩

Collections

UNIV-PARIS7 USPC
118 Consultations
59 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More