Well-posedness of an interaction model on Riemannian manifolds

Razvan C. Fetecau (1) , Francesco S. Patacchini (2)

1 SFU.ca - Simon Fraser University = Université Simon Fraser
2 IFPEN - IFP Energies nouvelles

We investigate a model for collective behaviour with intrinsic interactions on smooth Riemannian manifolds. For regular interaction potentials, we establish the local well-posedness of measure-valued solutions defined via optimal mass transport. We also extend our result to the global well-posedness of solutions for manifolds with nonpositive bounded sectional curvature. The core concept underlying the proofs is that of Lipschitz continuous vector fields in the sense of parallel transport.

Mots clés: Intrinsic interactions; measure solutions; swarming on manifolds; parallel transport; Lipschitz continuity

Domaines: Mathématiques [math]

Razvan C. Fetecau, Francesco S. Patacchini. Well-posedness of an interaction model on Riemannian manifolds. Communications on Pure and Applied Analysis, 2022, 21 (11), pp.3559-3585. ⟨10.3934/cpaa.2022114⟩. ⟨hal-03877707v1⟩