Stability of trajectories for N -particles dynamics with singular potential

Julien Barré 1 Maxime Hauray 2 Pierre-Emmanuel Jabin 1, 3
3 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
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Julien Barré, Maxime Hauray, Pierre-Emmanuel Jabin. Stability of trajectories for N -particles dynamics with singular potential. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2010, 2010 (7), pp.P07005. ⟨10.1088/1742-5468/2010/07/P07005⟩. ⟨hal-00472158⟩

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