Derivation of the linear Boltzmann equation without cut-off starting from particles
Ayi, Nathalie1
1 Sorbonne Universités UPMC Université Paris 06 UMR 7598 Laboratoire Jacques-Louis Lions F-75005, Paris, France
Journées équations aux dérivées partielles (2017), Exposé no. 1, 12 p.

We provide a rigorous derivation of the linear Boltzmann equation without cut-off 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to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford’s strategy.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.

Publié le :
DOI : 10.5802/jedp.651
Ayi, Nathalie 1

1 Sorbonne Universités UPMC Université Paris 06 UMR 7598 Laboratoire Jacques-Louis Lions F-75005, Paris, France 
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Ayi, Nathalie. Derivation of the linear Boltzmann equation without cut-off starting from particles. Journées équations aux dérivées partielles (2017), Exposé no. 1, 12 p. doi : 10.5802/jedp.651. http://archive.numdam.org/articles/10.5802/jedp.651/

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