An Intrinsic Aggregation Model on the Special Orthogonal Group SO(3): Well-posedness and Collective Behaviours

We investigate an aggregation model with intrinsic interactions on the special orthogonal group $SO(3)$. consider a smooth interaction potential that depends squared distance, and establish local global existence of measure-valued solutions to via optimal mass transport techniques. also study long-time behaviours such solutions, where we present sufficient conditions for formation asymptotic consensus. The analytical results are illustrated numerical experiments exhibit various patterns.