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Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum

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Abstract

We consider a system ofN hard disks in ℝ2 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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Communicated by J.L. Lebowitz

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Illner, R., Pulvirenti, M. Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum. Commun.Math. Phys. 105, 189–203 (1986). https://doi.org/10.1007/BF01211098

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  • DOI: https://doi.org/10.1007/BF01211098

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