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Boltzmann–Grad Limits for Stochastic Hard Sphere Models

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Abstract

We study a d-dimensional stochastic particle system in which the particles travel deterministically in between stochastic collisions. The collisions are elastic and occur with a probability of order ɛα when two particles are at a distance less than ɛ. When the number of particles N goes to infinity and Nɛd+α−1 goes to a nonzero constant, we show that the particle density converges to a solution of the Boltzmann equation provided that α≥d+1.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, California, 94720–3840, USA

    Fraydoun Rezakhanlou

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  1. Fraydoun Rezakhanlou
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H.-T. Yau

Research supported in part by NSF Grant DMS-00-72666.

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Rezakhanlou, F. Boltzmann–Grad Limits for Stochastic Hard Sphere Models. Commun. Math. Phys. 248, 553–637 (2004). https://doi.org/10.1007/s00220-004-1101-z

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  • DOI: https://doi.org/10.1007/s00220-004-1101-z

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