The Enskog process for hard and soft potentials

  • Martin Friesen
  • Barbara Rüdiger
  • Padmanabhan SundarEmail author


The density of a moderately dense gas evolving in a vacuum is given by the solution of an Enskog equation. Recently we have constructed in Albeverio et al. (J Stat Phys 167:90–122, 2017) the stochastic process that corresponds to the Enskog equation under suitable conditions. The Enskog process is identified as the solution of a McKean–Vlasov equation driven by a Poisson random measure. In this work, we continue the study for a wider class of collision kernels that includes hard and soft potentials. Based on a suitable particle approximation of binary collisions, the existence of an Enskog process is established.


Enskog equation Enskog process Boltzmann equation Kinetic theory Mean-field equation Particle approximation 

Mathematics Subject Classification

35Q20 76P05 60H30 



We would like thank Errico Presutti and Mario Pulvirenti for useful discussions related to this work.


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Authors and Affiliations

  1. 1.Faculty of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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