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Noise prevents collapse of Vlasov--Poisson point charges

Abstract : We elucidate the effect of noise on the dynamics of N point charges in a Vlasov-Poisson model driven by a singular bounded interaction force. We show that a too simple noise does not impact the structure inherited from the deterministic case and, in particular, cannot prevent the emergence of coalescence. Inspired by the theory of random transport in passive scalars, we identify a class of random fields which generate random pulses that are chaotic enough to disorganize the deterministic structure and prevent any collapse of the particles. We thus obtain strong unique solvability of the stochastic model for any initial configuration of different point charges. Moreover, in the case where there are exactly two particles, we implement the "vanishing noise method" for determining the continuation of the deterministic model after collapse.
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https://hal.archives-ouvertes.fr/hal-00683127
Contributor : Francois Delarue <>
Submitted on : Thursday, July 5, 2012 - 9:49:14 AM
Last modification on : Thursday, March 5, 2020 - 12:20:07 PM
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François Delarue, Franco Flandoli, Dario Vincenzi. Noise prevents collapse of Vlasov--Poisson point charges. Communications on Pure and Applied Mathematics, Wiley, 2014, 67, pp.1700-1736. ⟨hal-00683127v2⟩

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