Two-dimensional pseudo-gravity model
Abstract
We analyze a simple macroscopic model describing the evolution of a cloud of particles confined in a magneto-optical trap. The behavior of the particles is mainly driven by self--consistent attractive forces. In contrast to the standard model of gravitational forces, the force field does not result from a potential; moreover, the non linear coupling is more singular than the coupling based on the Poisson equation. We establish the existence of solutions, under a suitable smallness condition on the total mass, or, equivalently, for a sufficiently large diffusion coefficient. When a symmetry assumption is fulfilled, the solutions satisfy strengthened estimates (exponential moments). We also investigate the convergence of the -particles description towards the PDE system in the mean field regime.
Cite
@article{arxiv.1610.01296,
title = {Two-dimensional pseudo-gravity model},
author = {Julien Barré and Dan Crisan and Thierry Goudon},
journal= {arXiv preprint arXiv:1610.01296},
year = {2016}
}