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Abstract: 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.
Fuente: Analysis and PDE, 2022, 15(1), 175-196
Publisher: Mathematical Sciences Publishers
Year of publication: 2022
No. of pages: 22
Publication type: Article
DOI: 10.2140/apde.2022.15.175
ISSN: 2157-5045,1948-206X
Publication Url: https://doi.org/10.2140/apde.2022.15.175
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DANIEL LEAR CLAVERAS
SHVYDKOY, ROMAN
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