Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum |
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| Authors: | Reinhard Illner Mario Pulvirenti |
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| Affiliation: | 1. Fachbereich Mathematik, Universit?t Kaiserslautern, Erwin-Schr?dinger-Stra?e, D-6750, Kaiserslautern, Federal Republic of Germany
2. Dipartimento di Matematica dell' Università “La Sapienza”, P.A. Moro, I-00185, Roma, Italy
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| Abstract: | We consider a system ofN hard disks in ?2 in the Boltzmann-Grad limit (i.e.N → ∞,d ↘ 0,N·d → λ?1>0, whered is the diameter of the disks). If λ is sufficiently small and if the joint distribution densities factorize at time zero, we prove that the time-evolved one-particle distribution converges for all times to the solution of the Boltzmann equation with the same initial datum. |
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