  A Fokker-Planck type equation for interacting particles with exclusion
principle is analysed. The nonlinear drift gives rise to mathematical
difficulties in controlling moments of the distribution function. Assuming
enough initial moments are finite, we can show the global existence of weak
solutions for this problem. The natural associated entropy of the equation is
the main tool to derive uniform in time a priori estimates for the kinetic
energy and entropy. As a consequence, long-time asymptotics in $L^1$ are
characterized by the Fermi-Dirac equilibrium with the same initial mass. This
result is achieved without rate for any constructed global solution and with
exponential rate due to entropy/entropy-dissipation arguments for initial data
controlled by Fermi-Dirac distributions. Finally, initial data below radial
solutions with suitable decay at infinity lead to solutions for which the
relative entropy towards the Fermi-Dirac equilibrium is shown to converge to
zero without decay rate.
