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arXiv · 2008.11826

An intrinsic aggregation model on the special orthogonal group $\mathrm{SO}(3)$: well-posedness and collective behaviours

Razvan C. Fetecau·Seung-Yeal Ha·Hansol Park
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Abstract

We investigate an aggregation model with intrinsic interactions on the special orthogonal group $SO(3)$. We consider a smooth interaction potential that depends on the squared intrinsic distance, and establish local and global existence of measure-valued solutions to the model 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. The analytical results are illustrated with numerical experiments that exhibit various asymptotic patterns.

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Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park. 2020-08-26. An intrinsic aggregation model on the special orthogonal group $\mathrm{SO}(3)$: well-posedness and collective behaviours. https://doi.org/10.1007/s00332-021-09732-2

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