The mean-field limit for the dynamics of large particle systems

By François Golse. 2003

138 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/56fc9357d778b1c65d6ede1f15a35abbd4a102cd

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In Condensed Matter Physics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Heterophilious Dynamics Enhances Consensus (2013, background): “We limit ourselves to a few classic general references on this topic [27, 57, 101] and a few recent references in the contexts of opinion hydrodynamics [18, 105] and flocking hydrodynamics [21, 22, 40, 61, 73, 84, 88].”
From Newton to Boltzmann: Hard Spheres and Short-range Potentials (2012, result): “We refer to [11, 41] for pioneering results, to [25] for a recent study and to [21] for a review on that topic.”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, background): “This argument was detailed in a nice summer school notes in [42].”
On the Dynamics of Large Particle Systems in the Mean Field Limit (2013, methodology): “My earlier notes [42] contain a sketch of the proof of the mean field limit leading to the time-dependent Hartree-Fock equations; the interested reader is referred to [42] for more details in this direction.”
A well-posedness theory in measures for some kinetic models of collective motion (2009, methodology): “Such an approach was done for the Vlasov equation in classical kinetic theory [27, 4, 14, 31] with several nice reviews in [28, 32, 17].”
Particle, kinetic, and hydrodynamic models of swarming (2010, background): “Let us emphasize that the main technical issue is to overcome the lack of global Lipschitz character of the fields in phase space not allowing for direct application of known results [7,29,35,54,55,61,62].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Mathematical modeling of the collective behavior of individuals, such as swarming, has also been treated by continuum models steaming from discrete particle models [33] [14] [41] [34] [42] [15] [36] [13] [21] [23] [16] [17].”
Double milling in self-propelled swarms from kinetic theory (2009, background): “[3, 23] and also [4, 15, 28, 25, 26, 30, 31, 17] for applications to other physical systems and a rigorous analysis of related models.”
Stationary states of quadratic diffusion equations with long-range attraction (2011, unknown): “[43, 44] respectively [26] for general background).”