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From Particle Systems to the Landau Equation: A Consistency Result

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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 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 terms 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.

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Authors and Affiliations

  1. Department of Mathematics, Karlstad University, 65188, Karlstad, Sweden

    A. V. Boblylev

  2. Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro, 5, 00185, Roma, Italy

    M. Pulvirenti & C. Saffirio

Authors
  1. A. V. Boblylev
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  2. M. Pulvirenti
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  3. C. Saffirio
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Correspondence to M. Pulvirenti.

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Communicated by H. Spohn

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Boblylev, A.V., Pulvirenti, M. & Saffirio, C. From Particle Systems to the Landau Equation: A Consistency Result. Commun. Math. Phys. 319, 683–702 (2013). https://doi.org/10.1007/s00220-012-1633-6

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