Abstract. 
The Kuramoto model is the archetype of heterogeneous systems of
(globally) coupled oscillators with dissipative dynamics. In the continuum
limit, the order parameter that quantifies the population synchrony decays
to 0 in time, as long as the interaction strength remains small (so that
the uniformly distributed stationary solution remains stable). While this
phenomenon has been identified since the first studies, its proof remained
to be provided (most studies in the literature are limited to the
linearized dynamics).

In this talk, I will present rigorous results on damping of the order
parameter, both for the continuum limit and for finite size systems.
Joint work with D. Gérard-Varet and G. Giacomin