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

Young Pil Choi, Jan Haskovec

Research output: Contribution to journalArticle

1 Citation (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 languageEnglish
Pages (from-to)2660-2685
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number3
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Time Delay
Hydrodynamics
Time delay
Flocking
Euler System
Critical Phenomena
Communication
Classical Solution
Information Processing
Alignment
Formulation
Sufficient Conditions
Model

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Hydrodynamic cucker-smale model with normalized communication weights and time delay. / Choi, Young Pil; Haskovec, Jan.

In: SIAM Journal on Mathematical Analysis, Vol. 51, No. 3, 01.01.2019, p. 2660-2685.

Research output: Contribution to journalArticle

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