On the speed of approach to equilibrium for a collisionless gas

Kazuo Aoki (1) , François Golse (2, 3)

1 Department of Mechanical Engineering and Science
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 LJLL - Laboratoire Jacques-Louis Lions

We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform, constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We establish lower bounds for potential decay rates assuming uniform $L^p$ bounds on the initial distribution function. We also obtain a decay estimate in the spherically symmetric case. We discuss with particular care the influence of low-speed particles on thermalization by the wall.

Mots clés: Free-molecular gas; Approach to equilibrium; Diffuse reflection; Kinetic theory of gases

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Kazuo Aoki, François Golse. On the speed of approach to equilibrium for a collisionless gas. Kinet. Relat. Models, 2011, 4 (1), pp.87-107. ⟨10.3934/krm.2011.4.87⟩. ⟨hal-00517886⟩