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.
Bibliographical noteFunding 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 (email@example.com). \ddagger Computer, Electrical and Mathematical Sciences \& Engineering, King Abdullah University of Science and Technology, 23955 Thuwal, KSA (firstname.lastname@example.org).
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics