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


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.


Neural Network Statistical Physic Complex System Initial Data Distribution Density 
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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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