On weak solutions to the kinetic Cucker–Smale model with singular communication weights
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- by Young-Pil Choi and Jinwook Jung;
- Proc. Amer. Math. Soc. 152 (2024), 3423-3436
- DOI: https://doi.org/10.1090/proc/16837
- Published electronically: June 6, 2024
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Abstract:
We establish the local-in-time existence of weak solutions to the kinetic Cucker–Smale model with singular communication weights $\phi (x) = |x|^{-\alpha }$ with $\alpha \in (0,d)$. In the case $\alpha \in (0, d-1]$, we also provide the uniqueness of weak solutions extending the work of Carrillo et al [MMCS, ESAIM Proc. Surveys, vol. 47, EDP Sci., Les Ulis, 2014, pp. 17–35] where the existence and uniqueness of weak solutions are studied for $\alpha \in (0,d-1)$.References
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Bibliographic Information
- Young-Pil Choi
- Affiliation: Department of Mathematics, Yonsei University, 50 Yonsei-Ro, Seodaemun-Gu, Seoul 03722, Republic of Korea
- MR Author ID: 919090
- Email: ypchoi@yonsei.ac.kr
- Jinwook Jung
- Affiliation: Department of Mathematics and Research Institute for Natural Sciences, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea
- MR Author ID: 1253711
- ORCID: 0009-0001-8664-1188
- Email: jinwookjung@hanyang.ac.kr
- Received by editor(s): January 8, 2023
- Received by editor(s) in revised form: January 17, 2024
- Published electronically: June 6, 2024
- Additional Notes: The first author was supported by National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2022R1A2C1002820). The second author was supported by NRF grant (No. RS-2022-00165600).
The second author is the corresponding author. - Communicated by: Ryan Hynd
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 3423-3436
- MSC (2020): Primary 35D30, 35Q92
- DOI: https://doi.org/10.1090/proc/16837
- MathSciNet review: 4767273