On weak solutions to the kinetic Cucker–Smale model with singular communication weights

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16837

Young-Pil Choi, Jinwook Jung

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引用次数: 0

Abstract

We establish the local-in-time existence of weak solutions to the kinetic Cucker–Smale model with singular communication weights ϕ ( x ) = | x | − α \phi (x) = |x|^{-\alpha } with α ∈ ( 0 , d ) \alpha \in (0,d) . In the case α ∈ ( 0 , d − 1 ] \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 α ∈ ( 0 , d − 1 ) \alpha \in (0,d-1) .

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关于具有奇异通信权重的动力学卡克-斯马尔模型的弱解

我们建立了具有奇异通信权重 ϕ ( x ) = | x | - α \phi (x) = |x|^{-\alpha } 且 α ∈ ( 0 , d ) \alpha \ in (0,d) 的动力学 Cucker-Smale 模型弱解的局部时间内存在性。在 α∈ ( 0 , d - 1 ] 的情况下 \(0, d-1] . 我们还提供了弱解的唯一性，扩展了 Carrillo 等人的工作[MMCS, ESAIM Proc. Surveys, vol. 47, EDP Sci., Les Ulis, 2014, pp.

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.