  We study the long-time hydrodynamic behavior of systems of multi-species
which arise from agent-based description of alignment dynamics. The interaction
between species is governed by an array of symmetric communication kernels. We
prove that the crowd of different species flock towards the mean velocity if
(i) cross-interactions form a heavy-tailed connected array of kernels, while
(ii) self-interactions are governed by kernels with singular heads. The main
new aspect here, is that flocking behavior holds without closure assumption on
the specific form of pressure tensors. Specifically, we prove the long-time
flocking behavior for connected arrays of multi-species, with self-interactions
governed by entropic pressure laws [E. Tadmor, Swarming: hydrodynamic alignment
with pressure, ArXiv 2208.11786, (2022)] and driven by fractional
$p$-alignment. In particular, it follows that such multi-species hydrodynamics
approaches a mono-kinetic description. This generalizes the mono-kinetic,
"pressure-less" study in [S. He and E. Tadmor, A game of alignment: collective
behavior of multi-species, AIHP (c) Non Linear Anal. 38(4) (2021) 1031-1053.]
