Hydrodynamic cucker-smale model with normalized communication weights and time delay

Young Pil Choi; Jan Haskovec

doi:10.1137/17M1139151

Hydrodynamic cucker-smale model with normalized communication weights and time delay

Young Pil Choi, Jan Haskovec

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time-delayed nonlocal alignment forces. We resort to its Lagrangian formulation and prove the existence of its global-in-time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-/two-dimensional setting.

Original language	English
Pages (from-to)	2660-2685
Number of pages	26
Journal	SIAM Journal on Mathematical Analysis
Volume	51
Issue number	3
DOIs	https://doi.org/10.1137/17M1139151
Publication status	Published - 2019

Bibliographical note

Funding Information:
\ast Received by the editors July 17, 2017; accepted for publication (in revised form) April 8, 2019; published electronically June 25, 2019. http://www.siam.org/journals/sima/51-3/M113915.html Funding: The first author's research was supported by National Research Foundation of Korea (NRF) grants 2017R1C1B2012918 and 2017R1A4A1014735 funded by the Korean government (MSIP), by a POSCO Science Fellowship of the POSCO TJ Park Foundation, and by the Alexander Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers. The second author's research was supported by KAUST baseline funds and KAUST grant 1000000193. \dagger Department of Mathematics and Institute of Applied Mathematics, Inha University, Incheon 402-751, Republic of Korea (ypchoi@inha.ac.kr). \ddagger Computer, Electrical and Mathematical Sciences \& Engineering, King Abdullah University of Science and Technology, 23955 Thuwal, KSA (jan.haskovec@kaust.edu.sa).

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

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abstract = "We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time-delayed nonlocal alignment forces. We resort to its Lagrangian formulation and prove the existence of its global-in-time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-/two-dimensional setting.",

author = "Choi, {Young Pil} and Jan Haskovec",

note = "Funding Information: \ast Received by the editors July 17, 2017; accepted for publication (in revised form) April 8, 2019; published electronically June 25, 2019. http://www.siam.org/journals/sima/51-3/M113915.html Funding: The first author's research was supported by National Research Foundation of Korea (NRF) grants 2017R1C1B2012918 and 2017R1A4A1014735 funded by the Korean government (MSIP), by a POSCO Science Fellowship of the POSCO TJ Park Foundation, and by the Alexander Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers. The second author's research was supported by KAUST baseline funds and KAUST grant 1000000193. \dagger Department of Mathematics and Institute of Applied Mathematics, Inha University, Incheon 402-751, Republic of Korea (ypchoi@inha.ac.kr). \ddagger Computer, Electrical and Mathematical Sciences \& Engineering, King Abdullah University of Science and Technology, 23955 Thuwal, KSA (jan.haskovec@kaust.edu.sa). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics.",

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PY - 2019

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N2 - We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time-delayed nonlocal alignment forces. We resort to its Lagrangian formulation and prove the existence of its global-in-time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-/two-dimensional setting.

AB - We study a hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time-delayed nonlocal alignment forces. We resort to its Lagrangian formulation and prove the existence of its global-in-time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-/two-dimensional setting.

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Hydrodynamic cucker-smale model with normalized communication weights and time delay

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