  We consider the so-called spatially homogenous Kolmogorov-Vicsek model, a
non-linear Fokker-Planck equation of self-driven stochastic particles with
orientation interaction under the space-homogeneity. We prove the global
existence and uniqueness of weak solutions to the equation. We also show that
weak solutions exponentially converge to a steady state, which has the form of
the Fisher-von Mises distribution.
