These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order models for swarming. We focus on the question of passing from the discrete to the continuum model in the Dobrushin framework. We show how to use related techniques from fluid mechanics equations applied to first order models for swarming, also called the aggregation equation. We give qualitative bounds on the approximation of initial data by particles to obtain the mean-field limit for radial singular (at the origin) potentials up to the Newtonian singularity. We also show the propagation of chaos for more restricted set of singular potentials.
|Title of host publication||CISM International Centre for Mechanical Sciences, Courses and Lectures|
|Publisher||Springer International Publishing|
|Number of pages||46|
|Publication status||Published - 2014|
|Name||CISM International Centre for Mechanical Sciences, Courses and Lectures|
Bibliographical noteFunding Information:
JAC was partially supported by the project MTM2011-27739-C04-02 DGI (Spain) and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. JAC acknowledges support from the Royal Society by a Wolfson Research Merit Award. YPC was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (ref. 2012R1A6A3A03039496). JAC and YPC were supported by Engineering and Physical Sciences Research Council grants with references EP/K008404/1 (individual grant) and EP/I019111/1 (platform grant).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications