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 attraction-repulsion. In- troducing various scalings, the effects of the alignment and attraction-repulsion interactions give rise to a variety of hydrodynamic limits. For instance, local alignment produces a pressure term at the hydrodynamic limit whereas near-local alignment induces a viscosity term. Depending on the scal- ings, attraction-repulsion either yields an additional pressure term or a capillary force (also termed 'Korteweg force'). The hydrodynamic limits 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.