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Abstract: In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels ?(x): = |x|-(n+?) for ? ? (0,2). The solutions describe unidirectional parallel motion of agents governing multi-dimensional collective behavior of flocks. Here, we consider the range 1 < 2 and establish the global regularity of smooth solutions, together with a full description of their long-time dynamics. Specifically, we develop the flocking theory of these solutions and show long-time convergence to traveling wave with rapidly aligned velocity field.
Fuente: Communications in Mathematical Sciences, 2021, 19(3), 807-828
Editorial: International Press
Año de publicación: 2021
Nº de páginas: 20
Tipo de publicación: Artículo de Revista
DOI: 10.4310/CMS.2021.v19.n3.a11
ISSN: 1539-6746,1945-0796
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DANIEL LEAR CLAVERAS
SHVYDKOY, ROMAN
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