Thursday, July 26, 2012

1207.5987 (Alexander V. Bobylev et al.)

From particle systems to the Landau equation: a consistency result    [PDF]

Alexander V. Bobylev, Mario Pulvirenti, Chiara Saffirio
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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