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We investigate an aggregation model with intrinsic interactions on thespecial orthogonal group $SO(3)$. We consider a smooth interaction potentialthat depends on the squared intrinsic distance, and establish local and globalexistence of measure-valued solutions to the model via optimal mass transporttechniques. We also study the long-time behaviours of such solutions, where wepresent sufficient conditions for the formation of asymptotic consensus. Theanalytical results are illustrated with numerical experiments that exhibitvarious asymptotic patterns.

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