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to the infinite range of the potential, a non-integrable singularity appears in the angular collision kernel, making no longer valid the single-use of Lanford’s strategy.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.
@article{JEDP_2017____A1_0,
author = {Ayi, Nathalie},
title = {Derivation of the linear {Boltzmann} equation without cut-off starting from particles},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:1},
pages = {1--12},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2017},
doi = {10.5802/jedp.651},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.651/}
}
TY - JOUR AU - Ayi, Nathalie TI - Derivation of the linear Boltzmann equation without cut-off starting from particles JO - Journées équations aux dérivées partielles N1 - talk:1 PY - 2017 SP - 1 EP - 12 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.651/ DO - 10.5802/jedp.651 LA - en ID - JEDP_2017____A1_0 ER -
%0 Journal Article %A Ayi, Nathalie %T Derivation of the linear Boltzmann equation without cut-off starting from particles %J Journées équations aux dérivées partielles %Z talk:1 %D 2017 %P 1-12 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.651/ %R 10.5802/jedp.651 %G en %F JEDP_2017____A1_0
Ayi, Nathalie. Derivation of the linear Boltzmann equation without cut-off starting from particles. Journées équations aux dérivées partielles (2017), Talk no. 1, 12 p. doi : 10.5802/jedp.651. http://www.numdam.org/articles/10.5802/jedp.651/
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