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The Kuramoto model is a mean-field model for the synchronisation behaviour ofoscillators, which exhibits Landau damping. In a recent work, the nonlinearstability of a class of spatially inhomogeneous stationary states was shownunder the assumption of analytic regularity. This paper proves the nonlinearLandau damping under the assumption of Sobolev regularity. The weakerregularity required the construction of a different more robust bootstrapargument, which focuses on the nonlinear Volterra equation of the orderparameter.

Stability of partially locked states in the Kuramoto model through Landau damping with Sobolev regularity