Young Researchers Workshop: Stochastic and deterministic methods in kinetic theory

Landau damping to partially locked states in the Kuramoto model

Helge Dietert

Paris 7 - Diderot


The Kuramoto model consists of globally coupled oscillators. Like the Vlasov equation it is a mean-field model. Both models show the remarkable stability mechanism through phase-mixing, which is also called Landau damping. In this talk, I will discuss this stability mechanism for partially locked states in the Kuramoto model, which are inhomogeneous and irregular equilibria. In particular, I will discuss our work (i) establishing an explicit criterion for spectral stability, (ii) showing nonlinear stability for analytic perturbations, and (iii) extending the result to Sobolev regular perturbations. The items (i) and (ii) have been done in collaboration with Bastien Fernandez David GĂ©rard-Varet and are available at arXiv:1606.04470