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@article{Barre:2019:tran/7638,
author = {Barre, J and Crisan, DO and Goudon, T},
doi = {tran/7638},
journal = {Transactions of the American Mathematical Society},
pages = {2923--2962},
title = {Two-dimensional pseudo-gravity model: particles motion in a non-potential singular force field},
url = {http://dx.doi.org/10.1090/tran/7638},
volume = {371},
year = {2019}
}

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TY  - JOUR
AB  - 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.
AU  - Barre,J
AU  - Crisan,DO
AU  - Goudon,T
DO  - tran/7638
EP  - 2962
PY  - 2019///
SN  - 0002-9947
SP  - 2923
TI  - Two-dimensional pseudo-gravity model: particles motion in a non-potential singular force field
T2  - Transactions of the American Mathematical Society
UR  - http://dx.doi.org/10.1090/tran/7638
UR  - http://hdl.handle.net/10044/1/58989
VL  - 371
ER  -

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