Quasi-Stationary States for Particle Systems in the Mean-Field Limit

摘要

We prove that the N particles approximation of a class of stable stationary solutions of the Vlasov equation is uniformly valid on a time scale N β for β>0 (explicitly given in various cases) much longer than the usual log N scale. The vortex blob method in dimension 2 is also discussed. The result applies to a class of stationary solutions more general than in a previous work.