Instabilities in the mean field limit

Abstract

Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a ${\mathcal{C}}^2$ smooth potential in any dimension. We prove that in the mean field limit $N\to +\infty$, the $N$ particles system displays instabilities in times of order $\log N$ for some configurations approximately distributed according to unstable homogeneous equilibria.

arXiv commentminor typos corrected; Journal of Statistical Physics, accepted

References in corpus (5)

• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Relaxation times of unstable states in systems with long range interactions
• The Vlasov-Poisson dynamics as the mean field limit of extended charges
• Stability issues in the quasineutral limit of the one-dimensional Vlasov-Poisson equation
• Stability of trajectories for N -particles dynamics with singular potential

Cited by in corpus (2)

• Long time estimates for the Vlasov-Maxwell system in the non-relativistic limit
• Nonlinear instability of inhomogeneous steady states solutions to the HMF Model