In this paper, we prove a stability result for measure perturbations of some class of stationary distributions of a Vlasov equation. We use this result to prove that the N particles approximation of these stationary distributions is uniformly valid on a time scale of order N(1/8) which is much longer than the usual log N scale. We also prove similar results for the approximation of the two-dimensional Euler equation by the vortex blob method.
Long Time Estimates in the Mean Field Limit / Caglioti, Emanuele; F., Rousset. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 190:3(2008), pp. 517-547. [10.1007/s00205-008-0157-x]
Long Time Estimates in the Mean Field Limit
CAGLIOTI, Emanuele;
2008
Abstract
In this paper, we prove a stability result for measure perturbations of some class of stationary distributions of a Vlasov equation. We use this result to prove that the N particles approximation of these stationary distributions is uniformly valid on a time scale of order N(1/8) which is much longer than the usual log N scale. We also prove similar results for the approximation of the two-dimensional Euler equation by the vortex blob method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
