A mean-field limit of the particle swarmalator model

Seung-Yeal Ha; Jinwook Jung; Jeongho Kim; Jinyeong Park; Xiongtao Zhang

doi:10.3934/krm.2021011

Article Contents

2021, Volume 14, Issue 3: 429-468. Doi: 10.3934/krm.2021011

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A mean-field limit of the particle swarmalator model

1.
Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, and Korea Institute for Advanced Study, Hoegiro 85, Seoul, 02455, Republic of Korea
2.
Research Institute of Basic Sciences, Seoul National University, Seoul, 08826, Republic of Korea
3.
Institute of New Media and Communications, Seoul National University, Seoul, 08826, Republic of Korea
4.
Department of Mathematics and Research Institute of Natural Sciences, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
5.
Center for Mathematical Sciences, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074, China

^* Corresponding author: Jinwook Jung
^* Corresponding author: Jinwook Jung

Received: May 31, 2020

Revised: October 31, 2020

Early access: March 2021

Published: June 2021

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Abstract

We present a mean-field limit of the particle swarmalator model introduced in [46] with singular communication weights. For a mean-field limit, we employ a probabilistic approach for the propagation of molecular chaos and suitable cut-offs in singular terms, which results in the validation of the mean-field limit. We also provide a local-in-time well-posedness of strong and weak solutions to the derived kinetic swarmalator equation.

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Mathematics Subject Classification: Primary: 70F45, 82C22, 92B25.

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