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 N-particles description towards the PDE system in the mean field regime.
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Submitted on : Wednesday, October 12, 2016 - 10:52:10 AM
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Julien Barre, Dan Crisan, Thierry Goudon. Two-dimensional pseudo-gravity model. 2016. ⟨hal-01379951⟩

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