Two-dimensional pseudo-gravity model

Julien Barre (1) , Dan Crisan (2) , Thierry Goudon (3)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Department of Mathematics [Imperial College London]
3 COFFEE - COmplex Flows For Energy and Environment

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 N-particles description towards the PDE system in the mean field regime.

Mots clés: Attractive forces; Convection–diffusion equations; Mean field regime

Domaines: Mathématiques [math]

Julien Barre, Dan Crisan, Thierry Goudon. Two-dimensional pseudo-gravity model. 2016. ⟨hal-01379951⟩