Global weak solutions exist for the continuum Kuramoto model with fractional Laplacian-type non-integrable kernels and relax exponentially to the phase average under suitable conditions.
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The singular continuum Kuramoto model exhibits complete phase synchronization in finite time for identical natural frequencies and practical synchronization for non-identical frequencies, with a rigorous graph limit from finite singular Kuramoto systems.
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Relaxation dynamics of the continuum Kuramoto model with non-integrable kernels
Global weak solutions exist for the continuum Kuramoto model with fractional Laplacian-type non-integrable kernels and relax exponentially to the phase average under suitable conditions.