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arXiv · 1207.5987

From particle systems to the Landau equation: a consistency result

Alexander V. Bobylev·Mario Pulvirenti·Chiara Saffirio
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Abstract

We consider a system of N classical particles, interacting via a smooth, short- range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey to the usual BBGKY hierarchy, are decomposed into two contributions: one small but strongly oscillating, the other hopefully smooth. Eliminating the first, we arrive to establish the dynamical problem in term of a new hierarchy (for the smooth part) involving a memory term. We show that the first order correction to the free flow converges, as N \rightarrow \infty, to the corresponding term associated to the Landau equation. We also show the related propagation of chaos.

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Alexander V. Bobylev, Mario Pulvirenti, Chiara Saffirio. 2012-07-25. From particle systems to the Landau equation: a consistency result. https://doi.org/10.1007/s00220-012-1633-6

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