The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles

François Golse

doi:10.3934/krm.2022001

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2022, Volume 15, Issue 3: 517-534. Doi: 10.3934/krm.2022001

This issue Previous Article Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition Next Article Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space

The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles

François Golse

CMLS, École polytechnique, 91128 Palaiseau Cedex, France

In memory of Prof. Robert T. Glassey (1946-2020)

Received: August 31, 2021

Revised: October 31, 2021

Published: June 2022

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Abstract

In this note, we propose a slightly different proof of Gallavotti's theorem ["Statistical Mechanics: A Short Treatise", Springer, 1999, pp. 48-55] on the derivation of the linear Boltzmann equation for the Lorentz gas with a Poisson distribution of obstacles in the Boltzmann-Grad limit.

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Mathematics Subject Classification: Primary: 82C40, 35Q20, 82C70; Secondary: 60K35, 60G55.

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References

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