  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 non-local 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-dimensional setting.
