Methods and Applications of Analysis
Volume 20 (2013)
Hydrodynamic models of self-organized dynamics: Derivation and existence theory
Pages: 89 – 114
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. Introducing 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 scalings, 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.
self-propelled particles, alignment dynamics, hydrodynamic limit, diffusion correction, weakly non-local interaction, symmetrizable hyperbolic system, energy method, local wellposedness, capillary force, Korteweg force, attraction-repulsion potential
2010 Mathematics Subject Classification
35K55, 35L60, 35Qxx, 82C05, 82C22, 82C70, 92D50