Existence and stability of unidirectional flocks in hydrodynamic Euler Alignment systems

• Published in: arXiv.org
• Main Authors: Lear, Daniel, Shvydkoy, Roman
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.11.2019
• Subjects: Alignment; Dimensional stability; Mathematics - Analysis of PDEs; Scale models; Traveling waves; Velocity distribution; Well posed problems
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1911.10661

In this note 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 multi-dimensional 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 traveling wave with rapidly aligned velocity field. In the context of multi-scale models introduced in \cite{ST-multi} 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.