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Communications in Mathematical Physics

, Volume 105, Issue 2, pp 189–203 | Cite as

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

  • Reinhard Illner
  • Mario Pulvirenti
Article

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.

Keywords

Neural Network Statistical Physic Complex System Initial Data Distribution Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Reinhard Illner
    • 1
  • Mario Pulvirenti
    • 2
  1. 1.Fachbereich MathematikUniversität KaiserslauternKaiserslauternFederal Republic of Germany
  2. 2.Dipartimento di Matematica dell' Università “La Sapienza”, P.A. MoroRomaItaly

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