Stability of trajectories for N -particles dynamics with singular potential

Julien Barré (1) , Maxime Hauray (2) , Pierre-Emmanuel Jabin (1, 3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 TOSCA - Simuler et calibrer des modèles stochastiques

We study the stability in finite times of the tra jectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two tra jectories whose initial positions in phase space are close, remain close enough at later times. For potential less singular than the classical electrostatic kernel, we are able to prove such a result, for initial positions/velocities distributed according to the Gibbs equilibrium of the system.

Domaines: Equations aux dérivées partielles [math.AP]

Julien Barré, Maxime Hauray, Pierre-Emmanuel Jabin. Stability of trajectories for N -particles dynamics with singular potential. Journal of Statistical Mechanics: Theory and Experiment, 2010, 2010 (7), pp.P07005. ⟨10.1088/1742-5468/2010/07/P07005⟩. ⟨hal-00472158⟩