Two-dimensional pseudo-gravity model

Julien Barré; Dan Crisan; Thierry Goudon

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arXiv · 1610.01296

Two-dimensional pseudo-gravity model

Julien Barré·Dan Crisan·Thierry Goudon

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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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Julien Barré, Dan Crisan, Thierry Goudon. 2016-10-05. Two-dimensional pseudo-gravity model. https://arxiv.org/abs/1610.01296

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