Particles approximations of Vlasov equations with singular forces : Propagation of chaos

By Pierre-Emmanuel Jabin, M. Hauray. 2011

137 citations recorded by the source corpus.

We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger but close to one, in which case it allows for very small cut-off.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0506ab1e7d6e6d28f1af1517c0ea560e4a7a3337

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In Applied Mathematics

In Astronomy and Astrophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Mean Field Limit for Stochastic Particle Systems (2017, background): “For some recent progress in that direction, we refer to [42, 54, 55].”
Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces (2015, background): “The only results for deterministic second order systems with singular (non-Lipschitz) kernels without truncation are [27] and the more recent [28] for the propagation of chaos.”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, methodology): “This is the strategy that have been followed in [49] for the classical Vlasov equation and in [48] for Euler-like equations in ﬂuid mechanics.”