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On the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena

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  • Young-Pil Choi

    (Yonsei University)

Abstract

We study the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena, introduced by Choi and Lee (Math Models Methods Appl Sci 30: 2175–2227, 2020), which is pressureless Euler equations with nonlocal interaction forces. We present two different ways of deriving that hydrodynamic model. We first discuss the asymptotic analysis for the inertial kinetic Kuramoto equation with a strong local frequency alignment force. We show that a weak solution to the kinetic equation converges to the classical solution of that hydrodynamic synchronization model under certain assumptions on the initial data. We also provide the derivation from the particle Kuramoto model with inertia as the number of oscillators goes to infinity in the mono-kinetic case. Our proofs are based on a modulated energy-type estimate combined with the bounded Lipschitz distance between local densities.

Suggested Citation

  • Young-Pil Choi, 2023. "On the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena," Partial Differential Equations and Applications, Springer, vol. 4(1), pages 1-20, February.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:1:d:10.1007_s42985-022-00219-7
    DOI: 10.1007/s42985-022-00219-7
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    References listed on IDEAS

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    1. Alessandro Pluchino & Vito Latora & Andrea Rapisarda, 2005. "Changing Opinions In A Changing World: A New Perspective In Sociophysics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 515-531.
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