We reveal new classes of solutions to hydrodynamic Euler alignment systems
governing collective behavior of flocks. The solutions describe unidirectional parallel
motion of agents and are globally well-posed in multidimensional settings subject to a
threshold condition similar to the one-dimensional case. We develop the flocking and
stability theory of these solutions and show long-time convergence to a traveling wave
with rapidly aligned velocity field.
In the context of multiscale models introduced by Shvydkoy and Tadmor
(Multiscale Model. Simul. 19:2 (2021), 1115–1141) our solutions can be superimposed
into Mikado formations — clusters of unidirectional flocks pointing in various
directions. Such formations exhibit multiscale alignment phenomena and resemble
realistic behavior of interacting large flocks.
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