The Enskog Process

The existence of a weak solution to a McKean–Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique, when the dens...

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Bibliographic Details
Published in:Journal of statistical physics 2017-04, Vol.167 (1), p.90-122
Main Authors: Albeverio, S., Rüdiger, B., Sundar, P.
Format: Article
Language:English
Subjects:
Density
Differential equations
Kinetic theory
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:The existence of a weak solution to a McKean–Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique, when the density exists. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1743-9