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Long-time dynamics for a simple aggregation equation on the sphere

Frouvelle, Amic; Liu, Jian-Guo (2019), Long-time dynamics for a simple aggregation equation on the sphere, in Giacomin, G., Olla, S., Saada, E., Spohn, H., Stoltz, G. (eds), Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282, Springer : Berlin Heidelberg, p. 457-479. 10.1007/978-3-030-15096-9_16

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Type
Chapitre d'ouvrage
Date
2019
Book title
Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282
Book author
Giacomin, G., Olla, S., Saada, E., Spohn, H., Stoltz, G. (eds)
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-030-15095-2
Pages
457-479
Publication identifier
Metadata
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Author(s)
Frouvelle, Amic cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Liu, Jian-Guo
Duke Physics
Abstract (EN)
We give a complete study of the asymptotic behavior of a simple model of alignment of unit vectors, both at the level of particles , which corresponds to a system of coupled differential equations, and at the continuum level, under the form of an aggregation equation on the sphere. We prove unconditional convergence towards an aligned asymptotic state. In the cases of the differential system and of symmetric initial data for the partial differential equation, we provide precise rates of convergence.
Subjects / Keywords
alignment; unit vectors; aggregation equation