See the original proceeding notice from the Numdam source
We consider systems of particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both results will be a direct consequence of a weak-strong stability result on the one dimensional Vlasov-Poisson equation that is interesting by it own. We also prove the existence of global solutions to the particles dynamic starting from any initial positions and velocities, and the existence of global solutions to the Vlasov-Poisson equation starting from any measures with bounded first moment in velocity.
Hauray, Maxime. Mean field limit for the one dimensional Vlasov-Poisson equation. Séminaire Laurent Schwartz — EDP et applications (2012-2013), Talk no. 21, 16 p.. doi: 10.5802/slsedp.47
@article{SLSEDP_2012-2013____A21_0,
author = {Hauray, Maxime},
title = {Mean field limit for the one dimensional {Vlasov-Poisson~equation}},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:21},
pages = {1--16},
year = {2012-2013},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
doi = {10.5802/slsedp.47},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/slsedp.47/}
}
TY - JOUR AU - Hauray, Maxime TI - Mean field limit for the one dimensional Vlasov-Poisson equation JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:21 PY - 2012-2013 SP - 1 EP - 16 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://geodesic.mathdoc.fr/articles/10.5802/slsedp.47/ DO - 10.5802/slsedp.47 LA - en ID - SLSEDP_2012-2013____A21_0 ER -
%0 Journal Article %A Hauray, Maxime %T Mean field limit for the one dimensional Vlasov-Poisson equation %J Séminaire Laurent Schwartz — EDP et applications %Z talk:21 %D 2012-2013 %P 1-16 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://geodesic.mathdoc.fr/articles/10.5802/slsedp.47/ %R 10.5802/slsedp.47 %G en %F SLSEDP_2012-2013____A21_0
Cited by Sources: