From Newton's law to the linear Boltzmann equation without cut-off - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2016

From Newton's law to the linear Boltzmann equation without cut-off

Abstract

We provide a rigorous derivation of the linear Boltzmann equation without cutoff starting from a system of particles interacting via a potential with infinite range as the number of particles N goes to infinity under the Boltzmann-Grad scaling. The main difficulty in our context is that, due to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford's strategy. Our proof relies then on a combination of Lanford's strategy, of tools developed recently by Bodineau, Gallagher and Saint-Raymond to study the collision process, and of new duality arguments to study the additional terms associated to the long-range interaction, leading to some explicit weak estimates.
Fichier principal
Vignette du fichier
Newton to Boltzmann (Ayi).pdf (515.38 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01279218 , version 1 (25-02-2016)

Identifiers

  • HAL Id : hal-01279218 , version 1

Cite

Nathalie Ayi. From Newton's law to the linear Boltzmann equation without cut-off. 2016. ⟨hal-01279218⟩
185 View
288 Download

Share

Gmail Mastodon Facebook X LinkedIn More