Two-dimensional pseudo-gravity model: Particles motion in a non-potential singular force field

Barré, Julien; Crisan, Dan; Goudon, Thierry

doi:10.1090/tran/7638

Two-dimensional pseudo-gravity model: Particles motion in a non-potential singular force field
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by Julien Barré, Dan Crisan and Thierry Goudon PDF

Trans. Amer. Math. Soc. 371 (2019), 2923-2962 Request permission

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 nonlinear 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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