The Mean Field Kinetic Equation for Interacting Particle Systems with NonLipschitz Force
Abstract
In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$particle Newtonian system. For $L^1\cap L^\infty$ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while the difficulties arising from the nonlocal nonlinear interaction are tackled appropriately using the AubinLions compact embedding theorem.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.02686
 Bibcode:
 2017arXiv170902686Y
 Keywords:

 Mathematics  Analysis of PDEs;
 35Q83
 EPrint:
 16 pages