I will describe 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. In addition to existence of uniqueness results of the model PDE, I will discuss the convergence of the particles description towards the solution of the PDE system in the mean field regime.
- PDE CDT Lunchtime Seminar