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Existence and
stability of unidirectional flocks in hydrodynamic Euler
alignment systems
Daniel Lear and Roman Shvydkoy |
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Vol. 15 (2022), No. 1, 175–196
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Abstract |
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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. |
Keywords
flocking, alignment, Cucker–Smale, Mikado solutions, Euler
alignment
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Mathematical Subject Classification 2010
Primary: 92D25
Secondary: 35Q35, 76N10
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Milestones
Received: 24 November 2019
Revised: 24 May 2020
Accepted: 15 September 2020
Published: 16 March 2022
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Authors |
| Daniel Lear | |
| Department of Mathematics,
Statistics, and Computer Science University of Illinois Chicago, IL United States |
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| Roman Shvydkoy | |
| Department of Mathematics,
Statistics, and Computer Science University of Illinois Chicago, IL United States |
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