Francis Filbet: Trend to equilibrium and diffusion limit for the inertial Kuramoto-Sakaguchi equation

Speaker
Francis Filbet, Universite Paul Sabatier

Abstract
In this talk I will be interested in the inertial Kuramoto-Sakaguchi equation for interacting oscillatory systems. On the one hand, we prove the convergence toward corresponding phase homogeneous stationary states in weighted Lebesgue norm sense when the coupling strength is small enough.  More precisely, when the noise intensity is sufficiently large, equilibrium of the inertial Kuramoto-Sakaguchi equation is asymptotically stable. For generic initial data, every solutions converges to equilibrium in weighted Sobolev norm sense. We show the convergence for a large class of functions and by providing a simple proof. On the other hand, we investigate the diffusion limit when all oscillators are identical.  Here we provide error estimates for the diffusion limit with respect to the mass m ≪ 1 using a simple proof by imposing slightly more regularity on the solution.