Bastien Fernandez (LPSM, Paris):
The mathematics of asymptotic stability in the Kuramoto model

Abstract: The Kuramoto model is the archetype of nonlinear heterogeneous systems of coupled oscillators. Its phenomenology (in the continuum limit) strongly relies on the nonlinear stability of its stationary states. To understand and to rigorously assert stability in this infinite-dimensional setting have been long-standing challenges, and show similar features of the Landau damping in the Vlasov equation. In this talk, I will review results on stability conditions and asymptotic stability of various stationary states, that mathematically confirm the intuited phenomenology and its dependence on parameters.