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TITLE An Intrinsic Aggregation Model on the Special Orthogonal Group SO(3): Well-posedness and Collective Behaviours
KIAS AUTHORS Ha, Seung-Yeal
JOURNAL JOURNAL OF NONLINEAR SCIENCE, 2021
ARCHIVE  
ABSTRACT We consider a model for collective behaviour on Riemannian manifolds, with interactions modelled through a smooth interaction potential that depends on the squared intrinsic distance. We pay particular attention to the model set up on the special orthogonal group SO(3). We establish local and global existence of measure-valued solutions to the model on SO(3) via optimal mass transport techniques. We also study the long-time behaviours of such solutions, where we present sufficient conditions for the formation of asymptotic consensus on SO(3). In addition, we investigate asymptotic consensus on more general manifolds. The analytical results are illustrated with numerical experiments that exhibit various asymptotic patterns.
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