# American Institute of Mathematical Sciences

March  2011, 4(1): 87-107. doi: 10.3934/krm.2011.4.87

## On the speed of approach to equilibrium for a collisionless gas

 1 Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 2 Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz, 91128 Palaiseau Cedex, France

Received  September 2010 Revised  November 2010 Published  January 2011

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.
Citation: Kazuo Aoki, François Golse. On the speed of approach to equilibrium for a collisionless gas. Kinetic & Related Models, 2011, 4 (1) : 87-107. doi: 10.3934/krm.2011.4.87
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