Hydrodynamic models of self-organized dynamics: derivation and existence theory

This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attractionrepulsion. The starting point is the kinetic model considered in [10] with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in [10], the non-local effects of the alignment and attraction-repulsion interactions can be kept in the hydrodynamic limit and result in extra pressure, viscosity terms and capillary force. The systems are shown to be symmetrizable hyperbolic systems with viscosity terms. A local-in-time existence result is proved in the 2D case for the viscous model and in the 3D case for the inviscid model. The proof relies on the energy method.