Landau Damping in the Kuramoto Model
Speaker: Helge Dietert, University Paris 7
Location: Warren Weaver Hall 524
Date: Tuesday, December 6, 2016, 11 a.m.
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 and David Gerard-Varet and are available at arXiv:1606.04470.