Mixing and Mixtures in Geo- and Biophysical Flows: A Focus on Mathematical Theory and Numerical Methods

Synchronization in the Kuramoto model

David Gerard-Varet

Paris Diderot University


The Kuramoto mean field equation is a popular model that describes a large population of coupled oscillators. Its popularity is due to the fact that it exhibits synchronization behaviour. Mathematically, it corresponds to the convergence of the phase distribution of the oscillator towards a Dirac mass, as time goes to infinity. Although identified for long, this convergence has remained widely unjustified from the mathematical point of view. We shall report on recent progress on this question, discussing similarities and differences with Landau damping for Vlasov equations. This is joint work with H. Dietert and B. Fernandez.