On strong local alignment in the kinetic Cucker-Smale model

Details On strong local alignment in the kinetic Cucker-Smale model On strong local alignment in the kinetic Cucker-Smale model

2012-02-20

arxiv.org/abs/1202.4344v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

In two recent papers the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was formally motivated in these papers as a limiting case of an alignment term proposed by Motsch and Tadmor. In this paper, we rigorously justify this limit, and show that the considered equation is indeed a limit of the Motsch-Tadmor model when the radius of interaction goes to zero. The analysis involves velocity averaging lemmas and several $L^p$ estimates.

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