Hydrodynamic Cucker-Smale Model with Normalized Communication Weights and Time Delay

Young-Pil Choi, Jan Haskovec

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 (US)
Pages (from-to)2660-2685
Number of pages26
JournalSIAM Journal on Mathematical Analysis
Issue number3
StatePublished - Jun 25 2019


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