From Particle Systems to the Landau Equations: A Consistency Result

Bobylev, Alexander,1947-Karlstads universitet,Avdelningen för matematik,Kinetisk teori (author)

From Particle Systems to the Landau Equations : A Consistency Result

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 →∞, to the corresponding term associated to the Landau equation. We also show the related propagation of chaos.

Pulvirenti, MarioDipartimento di Matematica Guido Castelnuovo, Università La Sapienza, Roma (author)
Saffirio, ChiaraDipartimento di Matematica Guido Castelnuovo, Università La Sapienza, Roma (author)
Karlstads universitetAvdelningen för matematik (creator_code:org_t)

In:Communications in Mathematical Physics: Springer319:3, s. 693-7020010-36161432-0916

By the author/editor: Bobylev, Alexand ...; Pulvirenti, Mari ...; Saffirio, Chiara

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