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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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