Publications [#347998] of Jian-Guo Liu

Papers Published

1. Frouvelle, A; Liu, JG, Long-Time Dynamics for a Simple Aggregation Equation on the Sphere, Springer Proceedings in Mathematics and Statistics, vol. 282 (January, 2019), pp. 457-479, ISBN 9783030150952 [doi] [reputed journal]
   (last updated on 2025/02/21)

   Abstract:
   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.