https://hal-polytechnique.archives-ouvertes.fr/hal-00767550Tsuji, TetsuroTetsuroTsujiDepartment of Mechanical Engineering and Science - Kyoto University [Kyoto]Aoki, KazuoKazuoAokiDepartment of Mechanical Engineering and Science - Kyoto University [Kyoto]Golse, FrançoisFrançoisGolseLJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche ScientifiqueCMLS - Centre de Mathématiques Laurent Schwartz - X - École polytechnique - CNRS - Centre National de la Recherche ScientifiqueRelaxation of a Free-Molecular Gas to Equilibrium Caused by Interaction with Vessel WallHAL CCSD2010Free-molecular gasApproach to equilibriumDiffuse reflectionKinetic theory of gases[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Golse, François2012-12-20 09:00:522022-06-26 05:32:432012-12-20 09:00:52enJournal articles10.1007/s10955-010-9997-51A free-molecular gas contained in a static vessel with a uniform temperature is considered. The approach of the velocity distribution function of the gas molecules from a given initial distribution to the uniform equilibrium state at rest is investigated numerically under the diffuse reflection boundary condition. This relaxation is caused by the interaction of gas molecules with the vessel wall. It is shown that, for a spherical vessel, the velocity distribution function approaches the final uniform equilibrium distribution in such a way that their difference decreases in proportion to an inverse power of time. This is slower than the known result for a rarefied gas with molecular collisions.